38 lines
1.3 KiB
R
38 lines
1.3 KiB
R
# Minimum distance test based on a transform
|
|
#
|
|
# Author: François Pelletier
|
|
###############################################################################
|
|
|
|
#' Minimum distance test based on a transform function of a random variable
|
|
#' @param param Set of parameters to test
|
|
#' @param data Individual data vector
|
|
#' @param t Transform variate
|
|
#' @param FUN Transform function (analytical)
|
|
#' @param empFUN Transform function (empirical)
|
|
#' @param alpha tolerance level
|
|
#' @return A list containing the chi-square statistic,
|
|
#' degree of freedom, hypothesis reject boolean and p.value
|
|
#'
|
|
#' @author François Pelletier
|
|
md.test <- function(param,data,t,FUN,empFUN,alpha=0.05)
|
|
{
|
|
n <- length(data)
|
|
# Weight matrix
|
|
Q <- MASS::ginv(outer(t,t,function(j,k) FUN(j+k,param)-FUN(j,param)*FUN(k,param)))
|
|
# Vector of differences
|
|
v <- sqrt(n) * (empFUN(t,data)-FUN(t,param))
|
|
md.stat <- t(v) %*% Q %*% v
|
|
# Compute the test statistic using chi-square distribution
|
|
p.value <- pchisq(md.stat,df<-length(t))
|
|
reject <- p.value >= alpha
|
|
# Print output
|
|
cat("Minimum distance test based on a transform\n\nTest statistic: ",md.stat,
|
|
"\nDegree of freedom: ",df,
|
|
"\nP-value: ",p.value,
|
|
"\nReject H0 with confidence level ",1-alpha,"?: ",reject)
|
|
# Create the return list
|
|
list(md.stat=md.stat,df=df,reject=reject,p.value=p.value)
|
|
}
|
|
|
|
|
|
|