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