ajout d'intervalle de confiance, test wald

R/Wald.Test.R

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+# Wald test for estimating equations
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' Wald test for estimating equations
+#' @param param Estimated parameters
+#' @param n Size of estimation sample
+#' @param R Matrix of linear coefficients of the constraints
+#' @param r vector of linear constants of the constraints
+#' @param eqn.covariance Covariance matrix of the estimating equations
+#' @param eqn.gradient Gradient matrix of the estimating equations
+#' @param alpha level of confidence
+#' @return A list containing the statistic, p-value and reject of the null hypothesis
+#' 
+#' @author François Pelletier
+Wald.Test <- function(param,n,R,r,eqn.covariance,eqn.gradient,alpha=0.05)
+{
+	wald.stat <- n * t(R %*% param - r) %*% 
+			ginv(R %*% eqn.gradient %*% eqn.covariance %*% 
+							t(eqn.gradient) %*% t(R)) %*% 
+			(R %*% param - r)
+	PV <- pchisq(wald.stat,nrow(R))
+	list(wald.stat=wald.stat, p.value=PV, reject=PV>1-alpha)
+}

R/confidence.interval.QEE.R

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+# Confidence interval for QEE estimates
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Confidence interval for QEE estimates
+#'
+#' Uses covariance.GEE
+#' @param param Vector of parameters of the distribution function
+#' @param covariance Covariance matrix
+#' @param alpha confidence level
+#' @return 3 line matrix with lower bound, estimate and upper bound
+#' 
+#' @author François Pelletier
+confidence.interval.QEE <- function(param,covariance,n,alpha=0.05)
+{
+	cbind(LOWER=param - sqrt(diag(covariance))*qt(alpha,n,lower=F),
+			ESTIMATE=param,
+			UPPER=param + sqrt(diag(covariance))*qt(alpha,n,lower=F))
+}

R/covariance.QEE.R

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+# Covariance matrix using the component matrix M and V from QEE
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Covariance matrix using the component matrix M and V from QEE
+#'
+#' Covariance matrix using the component matrix M and V from QEE
+#' @param M Gradient matrix
+#' @param V Covariance matrix of equations
+#' @param n Sample size
+#' @return Weighted covariance matrix
+#' @author François Pelletier
+covariance.QEE <- function(M,V,n) ## Omega
+{
+	ginv(M %*% ginv(V) %*% t(M))/n
+}

man/Wald.Test.Rd

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+\name{Wald.Test}
+\alias{Wald.Test}
+\title{Wald test for estimating equations}
+\usage{
+Wald.Test(param, n, R, r, eqn.covariance, eqn.gradient, alpha = 0.05)
+}
+\arguments{
+  \item{param}{Estimated parameters}
+
+  \item{n}{Size of estimation sample}
+
+  \item{R}{Matrix of linear coefficients of the
+  constraints}
+
+  \item{r}{vector of linear constants of the constraints}
+
+  \item{eqn.covariance}{Covariance matrix of the estimating
+  equations}
+
+  \item{eqn.gradient}{Gradient matrix of the estimating
+  equations}
+
+  \item{alpha}{level of confidence}
+}
+\value{
+A list containing the statistic, p-value and reject of the
+null hypothesis
+}
+\description{
+Wald test for estimating equations
+}
+\author{
+François Pelletier
+}
+

man/confidence.interval.QEE.Rd

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+\name{confidence.interval.QEE}
+\alias{confidence.interval.QEE}
+\title{Confidence interval for QEE estimates}
+\usage{
+confidence.interval.QEE(param, covariance, n, alpha = 0.05)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{covariance}{Covariance matrix}
+
+  \item{alpha}{confidence level}
+}
+\value{
+3 line matrix with lower bound, estimate and upper bound
+}
+\description{
+Uses covariance.GEE
+}
+\author{
+François Pelletier
+}
+

man/covariance.QEE.Rd

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+\name{covariance.QEE}
+\alias{covariance.QEE}
+\title{Covariance matrix using the component matrix M and V from QEE}
+\usage{
+covariance.QEE(M, V, n)
+}
+\arguments{
+  \item{M}{Gradient matrix}
+
+  \item{V}{Covariance matrix of equations}
+
+  \item{n}{Sample size}
+}
+\value{
+Weighted covariance matrix
+}
+\description{
+Covariance matrix using the component matrix M and V from
+QEE
+}
+\author{
+François Pelletier
+}
+