Modifications au rapport, ajout des tests
This commit is contained in:
François Pelletier
parent
9cb92e4e50
commit
979ccec758
13 changed files with 1927 additions and 71 deletions
1
.gitignore
vendored
1
.gitignore
vendored
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@ -27,5 +27,6 @@
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*.mtc
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*.mtc1
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*.out
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*.pdf
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*.synctex.gz
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/GAL-Buckle95-concordance.tex
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201
GAL-Buckle95.Rnw
201
GAL-Buckle95.Rnw
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@ -19,6 +19,8 @@
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\maketitle
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\tableofcontents
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\chapter{Initialisation}
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\section{Chargement des paquets}
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<<>>=
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setwd("~/git/GAL-Buckle95/")
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@ -56,17 +58,19 @@ n <- length(RETURNS)
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EppsPulley.test(RETURNS)
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@
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\chapter{Estimation}
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\section{Données mises à l'échelle}
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<<>>=
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scaledRETURNS <- as.vector(scale(RETURNS))
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sRET <- as.vector(scale(RETURNS))
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@
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\section{Première estimation par QEE}
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<<>>=
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## Point de départ
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pt.depart <- startparamGAL(scaledRETURNS)
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pt.depart <- startparamGAL(sRET)
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## Fonctions pour les moments
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meanQEE <- function(param) mGAL(param,1)
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varianceQEE <- function(param) cmGAL(param,2)
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@ -77,72 +81,197 @@ kurtosisQEE <- function(param) cmGAL(param,4)
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dmeanQEE <- function(param) dmGAL(param,1)
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dsdQEE <- function(param) dmGAL(param,2)
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## Estimation gaussienne
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optim1 <- optim(pt.depart,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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optim1 <- optim(pt.depart,obj.gauss,gr=NULL,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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pt.optim1 <- optim1$par
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## Estimation de crowder
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optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
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optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,sRET,
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meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
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pt.optim2 <- optim2$par
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## Estimation de crowder modifiée
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optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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pt.optim3 <- optim3$par
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@
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\section{Résultats de la première estimation par QEE}
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<<>>=
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cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
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V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
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confidence.interval.QEE(pt.optim1,cov.optim1,n)
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confidence.interval.QEE(pt.optim2,cov.optim2,n)
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confidence.interval.QEE(pt.optim3,cov.optim3,n)
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cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE),
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V.gauss(pt.optim1,sRET,meanQEE,varianceQEE,
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skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,sRET,
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varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder(pt.optim2,sRET,varianceQEE,
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skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,sRET,
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varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder.Mod(pt.optim3,sRET,varianceQEE,dmeanQEE,dsdQEE),n)
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confidence.interval.QEE(pt.optim1,cov.optim1,n)
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confidence.interval.QEE(pt.optim2,cov.optim2,n)
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confidence.interval.QEE(pt.optim3,cov.optim3,n)
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@
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\section{Seconde estimation par QEE}
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<<>>=
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## Estimation gaussienne
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optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
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ginv(V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
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optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE,
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ginv(V.gauss(pt.optim1,sRET,meanQEE,
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varianceQEE,skewnessQEE,kurtosisQEE,
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dmeanQEE,dsdQEE)))
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pt.optim4 <- optim4$par
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## Estimation de crowder
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optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
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ginv(V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
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optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,sRET,
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meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
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ginv(V.Crowder(pt.optim2,sRET,varianceQEE,skewnessQEE,
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kurtosisQEE,dmeanQEE,dsdQEE)))
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pt.optim5 <- optim5$par
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## Estimation de crowder modifiée
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optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
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ginv(V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE)))
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optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE,
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ginv(V.Crowder.Mod(pt.optim3,sRET,varianceQEE,
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dmeanQEE,dsdQEE)))
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pt.optim6 <- optim6$par
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@
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\section{Résultats de la seconde estimation par QEE}
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<<>>=
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cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
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V.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
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confidence.interval.QEE(pt.optim4,cov.optim4,n)
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confidence.interval.QEE(pt.optim5,cov.optim5,n)
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confidence.interval.QEE(pt.optim6,cov.optim6,n)
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cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,sRET,
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meanQEE,varianceQEE,dmeanQEE,dsdQEE),
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V.gauss(pt.optim4,sRET,meanQEE,varianceQEE,
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skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,sRET,
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varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder(pt.optim5,sRET,varianceQEE,skewnessQEE,
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kurtosisQEE,dmeanQEE,dsdQEE),n)
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cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,sRET,
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varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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V.Crowder.Mod(pt.optim6,sRET,varianceQEE,dmeanQEE,dsdQEE),n)
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confidence.interval.QEE(pt.optim4,cov.optim4,n)
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confidence.interval.QEE(pt.optim5,cov.optim5,n)
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confidence.interval.QEE(pt.optim6,cov.optim6,n)
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@
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\section{Estimation par GMM}
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<<>>=
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## GMM régulier
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optim7 <- optim.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
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meanf=meanQEE,variancef=varianceQEE)
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## GMM itératif
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optim8 <- iterative.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
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meanf=meanQEE,variancef=varianceQEE)
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## GMM régulier
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optim7 <- optim.GMM(pt.depart,
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conditions.vector=meanvariance.gmm.vector,
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data=sRET,W=diag(2),
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meanf=meanQEE,variancef=varianceQEE)
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pt.optim7 <- optim7$par
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cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*%
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covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET,
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meanf=meanQEE,variancef=varianceQEE) %*%
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t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n
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## GMM itératif
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optim8 <- iterative.GMM(pt.depart,
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conditions.vector=meanvariance.gmm.vector,
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data=sRET,W=diag(2),
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meanf=meanQEE,variancef=varianceQEE)
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pt.optim8 <- optim8$par
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cov.optim8 <- mean.variance.GMM.gradient.GAL(pt.optim8,sRET) %*%
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optim8$cov %*%
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t(mean.variance.GMM.gradient.GAL(pt.optim8,sRET)) / n
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confidence.interval.QEE(pt.optim7,cov.optim7,n)
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confidence.interval.QEE(pt.optim8,cov.optim8,n)
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@
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\chapter{Comparaison des résultats}
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<<>>=
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# Aggrégation des estimateurs (pour simplifier les calculs)
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pts.estim <- cbind(pt.optim1,pt.optim2,pt.optim3,pt.optim4,
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pt.optim5,pt.optim6,pt.optim7,pt.optim8)
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l.pts.estim <- as.list(data.frame(pts.estim))
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@
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\section{Fonction de répartition}
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<<>>=
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# Points d'évaluation
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xi <- seq(2*min(sRET),2*max(sRET),length.out=2^6)
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# Fonction de répartition par intégration de la fonction caractéristique
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dist1 <- cbind(cftocdf(xi,cfGAL,param=pt.optim1),
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cftocdf(xi,cfGAL,param=pt.optim2),
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cftocdf(xi,cfGAL,param=pt.optim3),
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cftocdf(xi,cfGAL,param=pt.optim4),
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cftocdf(xi,cfGAL,param=pt.optim5),
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cftocdf(xi,cfGAL,param=pt.optim6),
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cftocdf(xi,cfGAL,param=pt.optim7),
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cftocdf(xi,cfGAL,param=pt.optim8))
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# Fonction de répartition par point de selle
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dist2 <- cbind(psaddleapproxGAL(xi,pt.optim1),
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psaddleapproxGAL(xi,pt.optim2),
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psaddleapproxGAL(xi,pt.optim3),
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psaddleapproxGAL(xi,pt.optim4),
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psaddleapproxGAL(xi,pt.optim5),
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psaddleapproxGAL(xi,pt.optim6),
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psaddleapproxGAL(xi,pt.optim7),
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psaddleapproxGAL(xi,pt.optim8))
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# Fonction de répartition par intégration de la fonction de densité
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dist3 <- cbind(pGAL(xi,pt.optim1),
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pGAL(xi,pt.optim2),
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pGAL(xi,pt.optim3),
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pGAL(xi,pt.optim4),
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pGAL(xi,pt.optim5),
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pGAL(xi,pt.optim6),
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pGAL(xi,pt.optim7),
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pGAL(xi,pt.optim8))
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@
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\pagebreak
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\subsection{Graphiques}
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<<results=tex>>=
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for (i in 1:8)
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{
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file<-paste("dist-GAL-",i,".pdf",sep="")
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pdf(file=file,paper="special",width=6,height=6)
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plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
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lines(xi,dist1[,i],col="green")
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lines(xi,dist2[,1],col="red")
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lines(xi,dist3[,1],col="pink")
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lines(xi,pnorm(xi),type="l",col="blue")
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dev.off()
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cat("\\includegraphics[height=2in,width=2in]{",
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file,"}\n",sep="")
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}
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@
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\subsection{Statistiques}
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Test du $\chi^2$, Méthode avec intégration
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<<results=tex>>=
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chisquare.test1 <- function(param,DATA.hist,FUN,method)
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{
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chisquare.test(DATA.hist,FUN,param,method=method)
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}
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6)
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@
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Test du $\chi^2$, Méthode avec point de selle
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<<results=tex>>=
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6)
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@
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Statistique de Kolmogorov-Smirnov
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<<results=tex>>=
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ks.test1 <- function(param,x,y) ks.test(x,y,param)
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xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
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@
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Statistique de distance minimale
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<<results=tex>>=
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tvariate1 <- seq(-.1,.1,by=0.01)
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xtable(do.call(rbind,mclapply(l.pts.estim,md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
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@
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\end{document}
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BIN
GAL-Buckle95.pdf
BIN
GAL-Buckle95.pdf
Binary file not shown.
309
GAL-Buckle95.tex
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@ -19,6 +19,8 @@
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\maketitle
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\tableofcontents
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\chapter{Initialisation}
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\section{Chargement des paquets}
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\begin{Schunk}
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\begin{Sinput}
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@ -84,11 +86,13 @@ $Reject
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\end{Soutput}
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\end{Schunk}
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\chapter{Estimation}
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\section{Données mises à l'échelle}
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\begin{Schunk}
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\begin{Sinput}
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> scaledRETURNS <- as.vector(scale(RETURNS))
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> sRET <- as.vector(scale(RETURNS))
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\end{Sinput}
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\end{Schunk}
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@ -97,7 +101,7 @@ $Reject
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\begin{Schunk}
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\begin{Sinput}
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> ## Point de départ
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> pt.depart <- startparamGAL(scaledRETURNS)
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> pt.depart <- startparamGAL(sRET)
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> ## Fonctions pour les moments
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> meanQEE <- function(param) mGAL(param,1)
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> varianceQEE <- function(param) cmGAL(param,2)
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@ -108,13 +112,16 @@ $Reject
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> dmeanQEE <- function(param) dmGAL(param,1)
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> dsdQEE <- function(param) dmGAL(param,2)
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> ## Estimation gaussienne
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> optim1 <- optim(pt.depart,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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> optim1 <- optim(pt.depart,obj.gauss,gr=NULL,sRET,
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+ meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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> pt.optim1 <- optim1$par
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> ## Estimation de crowder
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> optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
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> optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,sRET,
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+ meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
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> pt.optim2 <- optim2$par
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> ## Estimation de crowder modifiée
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> optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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> optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,sRET,
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+ meanQEE,varianceQEE,dmeanQEE,dsdQEE)
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> pt.optim3 <- optim3$par
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\end{Sinput}
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\end{Schunk}
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@ -123,13 +130,18 @@ $Reject
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\begin{Schunk}
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\begin{Sinput}
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> cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
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+ V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
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> cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
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+ V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim1,cov.optim1,n)
|
||||
> cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,sRET,
|
||||
+ meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
+ V.gauss(pt.optim1,sRET,meanQEE,varianceQEE,
|
||||
+ skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,sRET,
|
||||
+ varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder(pt.optim2,sRET,varianceQEE,
|
||||
+ skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,sRET,
|
||||
+ varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim3,sRET,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim1,cov.optim1,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -139,7 +151,7 @@ $Reject
|
|||
[4,] 1.994757 2.021370 2.047982
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim2,cov.optim2,n)
|
||||
> confidence.interval.QEE(pt.optim2,cov.optim2,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -149,7 +161,7 @@ $Reject
|
|||
[4,] 1.839966 1.878296 1.916626
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim3,cov.optim3,n)
|
||||
> confidence.interval.QEE(pt.optim3,cov.optim3,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -165,16 +177,23 @@ $Reject
|
|||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> ## Estimation gaussienne
|
||||
> optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
> optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,sRET,
|
||||
+ meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.gauss(pt.optim1,sRET,meanQEE,
|
||||
+ varianceQEE,skewnessQEE,kurtosisQEE,
|
||||
+ dmeanQEE,dsdQEE)))
|
||||
> pt.optim4 <- optim4$par
|
||||
> ## Estimation de crowder
|
||||
> optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
> optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,sRET,
|
||||
+ meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder(pt.optim2,sRET,varianceQEE,skewnessQEE,
|
||||
+ kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
> pt.optim5 <- optim5$par
|
||||
> ## Estimation de crowder modifiée
|
||||
> optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE)))
|
||||
> optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,sRET,
|
||||
+ meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder.Mod(pt.optim3,sRET,varianceQEE,
|
||||
+ dmeanQEE,dsdQEE)))
|
||||
> pt.optim6 <- optim6$par
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
|
@ -183,13 +202,18 @@ $Reject
|
|||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
+ V.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim4,cov.optim4,n)
|
||||
> cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,sRET,
|
||||
+ meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
+ V.gauss(pt.optim4,sRET,meanQEE,varianceQEE,
|
||||
+ skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,sRET,
|
||||
+ varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder(pt.optim5,sRET,varianceQEE,skewnessQEE,
|
||||
+ kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,sRET,
|
||||
+ varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim6,sRET,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim4,cov.optim4,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -199,7 +223,7 @@ $Reject
|
|||
[4,] 1.995452 2.022048 2.048644
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim5,cov.optim5,n)
|
||||
> confidence.interval.QEE(pt.optim5,cov.optim5,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -209,7 +233,7 @@ $Reject
|
|||
[4,] 1.842116 1.880376 1.918636
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim6,cov.optim6,n)
|
||||
> confidence.interval.QEE(pt.optim6,cov.optim6,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
|
|
@ -224,14 +248,229 @@ $Reject
|
|||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> ## GMM régulier
|
||||
> optim7 <- optim.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
> ## GMM itératif
|
||||
> optim8 <- iterative.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
> ## GMM régulier
|
||||
> optim7 <- optim.GMM(pt.depart,
|
||||
+ conditions.vector=meanvariance.gmm.vector,
|
||||
+ data=sRET,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
> pt.optim7 <- optim7$par
|
||||
> cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*%
|
||||
+ covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET,
|
||||
+ meanf=meanQEE,variancef=varianceQEE) %*%
|
||||
+ t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n
|
||||
> ## GMM itératif
|
||||
> optim8 <- iterative.GMM(pt.depart,
|
||||
+ conditions.vector=meanvariance.gmm.vector,
|
||||
+ data=sRET,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
> pt.optim8 <- optim8$par
|
||||
> cov.optim8 <- mean.variance.GMM.gradient.GAL(pt.optim8,sRET) %*%
|
||||
+ optim8$cov %*%
|
||||
+ t(mean.variance.GMM.gradient.GAL(pt.optim8,sRET)) / n
|
||||
> confidence.interval.QEE(pt.optim7,cov.optim7,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.878702 -0.641646 -0.404589
|
||||
[2,] -0.469225 0.625908 1.721040
|
||||
[3,] -0.192234 0.326366 0.844965
|
||||
[4,] 1.696121 1.965995 2.235869
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim8,cov.optim8,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.874031 -0.636980 -0.399929
|
||||
[2,] -0.473292 0.626346 1.725984
|
||||
[3,] -0.193600 0.322895 0.839390
|
||||
[4,] 1.704166 1.972716 2.241265
|
||||
\end{Soutput}
|
||||
\end{Schunk}
|
||||
|
||||
\chapter{Comparaison des résultats}
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> # Aggrégation des estimateurs (pour simplifier les calculs)
|
||||
> pts.estim <- cbind(pt.optim1,pt.optim2,pt.optim3,pt.optim4,
|
||||
+ pt.optim5,pt.optim6,pt.optim7,pt.optim8)
|
||||
> l.pts.estim <- as.list(data.frame(pts.estim))
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Fonction de répartition}
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> # Points d'évaluation
|
||||
> xi <- seq(2*min(sRET),2*max(sRET),length.out=2^6)
|
||||
> # Fonction de répartition par intégration de la fonction caractéristique
|
||||
> dist1 <- cbind(cftocdf(xi,cfGAL,param=pt.optim1),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim2),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim3),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim4),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim5),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim6),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim7),
|
||||
+ cftocdf(xi,cfGAL,param=pt.optim8))
|
||||
> # Fonction de répartition par point de selle
|
||||
> dist2 <- cbind(psaddleapproxGAL(xi,pt.optim1),
|
||||
+ psaddleapproxGAL(xi,pt.optim2),
|
||||
+ psaddleapproxGAL(xi,pt.optim3),
|
||||
+ psaddleapproxGAL(xi,pt.optim4),
|
||||
+ psaddleapproxGAL(xi,pt.optim5),
|
||||
+ psaddleapproxGAL(xi,pt.optim6),
|
||||
+ psaddleapproxGAL(xi,pt.optim7),
|
||||
+ psaddleapproxGAL(xi,pt.optim8))
|
||||
> # Fonction de répartition par intégration de la fonction de densité
|
||||
> dist3 <- cbind(pGAL(xi,pt.optim1),
|
||||
+ pGAL(xi,pt.optim2),
|
||||
+ pGAL(xi,pt.optim3),
|
||||
+ pGAL(xi,pt.optim4),
|
||||
+ pGAL(xi,pt.optim5),
|
||||
+ pGAL(xi,pt.optim6),
|
||||
+ pGAL(xi,pt.optim7),
|
||||
+ pGAL(xi,pt.optim8))
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
\pagebreak
|
||||
\subsection{Graphiques}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> for (i in 1:8)
|
||||
+ {
|
||||
+ file<-paste("dist-GAL-",i,".pdf",sep="")
|
||||
+ pdf(file=file,paper="special",width=6,height=6)
|
||||
+ plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
|
||||
+ lines(xi,dist1[,i],col="green")
|
||||
+ lines(xi,dist2[,1],col="red")
|
||||
+ lines(xi,dist3[,1],col="pink")
|
||||
+ lines(xi,pnorm(xi),type="l",col="blue")
|
||||
+ dev.off()
|
||||
+ cat("\\includegraphics[height=2in,width=2in]{",
|
||||
+ file,"}\n",sep="")
|
||||
+ }
|
||||
\end{Sinput}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-1.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-2.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-3.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-4.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-5.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-6.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-7.pdf}
|
||||
\includegraphics[height=2in,width=2in]{dist-GAL-8.pdf}\end{Schunk}
|
||||
|
||||
\subsection{Statistiques}
|
||||
Test du $\chi^2$, Méthode avec intégration
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> chisquare.test1 <- function(param,DATA.hist,FUN,method)
|
||||
+ {
|
||||
+ chisquare.test(DATA.hist,FUN,param,method=method)
|
||||
+ }
|
||||
> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.2 by xtable 1.7-1 package
|
||||
% Sat Mar 15 11:38:58 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrr}
|
||||
\hline
|
||||
& chisquare.stat & df & p.value \\
|
||||
\hline
|
||||
pt.optim1 & 5.473824 & 6.000000 & 0.484626 \\
|
||||
pt.optim2 & 5.329673 & 6.000000 & 0.502277 \\
|
||||
pt.optim3 & 5.388158 & 6.000000 & 0.495076 \\
|
||||
pt.optim4 & 5.474310 & 6.000000 & 0.484567 \\
|
||||
pt.optim5 & 5.337004 & 6.000000 & 0.501372 \\
|
||||
pt.optim6 & 5.390662 & 6.000000 & 0.494769 \\
|
||||
pt.optim7 & 5.454256 & 6.000000 & 0.487003 \\
|
||||
pt.optim8 & 5.476963 & 6.000000 & 0.484245 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
Test du $\chi^2$, Méthode avec point de selle
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.2 by xtable 1.7-1 package
|
||||
% Sat Mar 15 11:38:58 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrr}
|
||||
\hline
|
||||
& chisquare.stat & df & p.value \\
|
||||
\hline
|
||||
pt.optim1 & 9.293574 & 6.000000 & 0.157728 \\
|
||||
pt.optim2 & 8.345592 & 6.000000 & 0.213862 \\
|
||||
pt.optim3 & 9.050625 & 6.000000 & 0.170751 \\
|
||||
pt.optim4 & 9.292836 & 6.000000 & 0.157767 \\
|
||||
pt.optim5 & 8.344140 & 6.000000 & 0.213959 \\
|
||||
pt.optim6 & 9.062381 & 6.000000 & 0.170100 \\
|
||||
pt.optim7 & 8.616379 & 6.000000 & 0.196330 \\
|
||||
pt.optim8 & 8.610490 & 6.000000 & 0.196698 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
Statistique de Kolmogorov-Smirnov
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> ks.test1 <- function(param,x,y) ks.test(x,y,param)
|
||||
> xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.2 by xtable 1.7-1 package
|
||||
% Sat Mar 15 11:38:58 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrrrr}
|
||||
\hline
|
||||
& statistic & p.value & alternative & method & data.name \\
|
||||
\hline
|
||||
pt.optim1 & 0.158220 & 0.171912 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim2 & 0.140346 & 0.289345 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim3 & 0.156772 & 0.179751 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim4 & 0.158159 & 0.172235 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim5 & 0.139916 & 0.292753 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim6 & 0.156960 & 0.178718 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim7 & 0.141230 & 0.282437 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
pt.optim8 & 0.140016 & 0.291954 & two-sided & One-sample Kolmogorov-Smirnov test & x \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
Statistique de distance minimale
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> tvariate1 <- seq(-.1,.1,by=0.01)
|
||||
> xtable(do.call(rbind,mclapply(l.pts.estim,md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.2 by xtable 1.7-1 package
|
||||
% Sat Mar 15 11:38:58 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrr}
|
||||
\hline
|
||||
& md.stat & df & p.value \\
|
||||
\hline
|
||||
pt.optim1 & 0.000422 & 21.000000 & 0.000000 \\
|
||||
pt.optim2 & 0.120174 & 21.000000 & 0.000000 \\
|
||||
pt.optim3 & 0.001384 & 21.000000 & 0.000000 \\
|
||||
pt.optim4 & 0.000388 & 21.000000 & 0.000000 \\
|
||||
pt.optim5 & 0.123295 & 21.000000 & 0.000000 \\
|
||||
pt.optim6 & 0.001451 & 21.000000 & 0.000000 \\
|
||||
pt.optim7 & 0.007980 & 21.000000 & 0.000000 \\
|
||||
pt.optim8 & 0.010416 & 21.000000 & 0.000000 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
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|
|
|
|||
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