R/mvshapetest_internal.R

In MNM: Multivariate Nonparametric Methods. An Approach Based on Spatial Signs and Ranks

#
mauchly.test <- function(X,location, n, p)
    {
    if (location=="est") S <- cov(X) else S <- covOrigin(X)
    L <- ((det(S) / (sum(diag(S))/p)^p ))^(n/2)
    names(L) <- "L"
    df <- (p+2)*(p-1)/2
    names(df)<-"df"
    p.value <- 1-pchisq(-2*log(L), df)
    METHOD<-"Mauchly test for sphericity"
    list(statistic=L, p.value = p.value, parameter = df, method = METHOD)
    }

#SSCov.test <- function(X, n, p)
#    {
#    cpp <- Cpp(p)
#    METHOD = "Test of sphericity based on TCOV"
#    TCOV <- SSCov(X)
#    vTCOV <- as.vector(TCOV)
#    cross <- SpatialNP:::Q2internal(X)
#    cov.cTCOV <- 4 * (matrix(cross[-(1:p^2)], ncol = p^2) -  tcrossprod(vTCOV)) /n
#    test.statistic <- as.vector(t(cpp %*% vTCOV) %*% Ginv(cov.cTCOV) %*% (cpp %*% vTCOV))
#    names(test.statistic) <- "Q2"
#    df <- (p+2)*(p-1)/2
#    names(df)<-"df"
#    p.value <- 1-pchisq(test.statistic, df)
#    METHOD<-"Test for sphericity based on TCOV"
#    list(statistic=test.statistic, p.value = p.value, parameter = df, method = METHOD)
#    }
    
SSCov.test <- function(X, n, p)
    {
    METHOD = "Test of sphericity based on TCOV"
    TEST <- sr.sphere.test(X, score="symmsign")
    
    test.statistic <- TEST$statistic
    names(test.statistic) <- "Q2"
    
    df <- TEST$parameter
    names(df)<-"df"
    
    p.value <- TEST$p.value
    
    list(statistic=test.statistic, p.value = p.value, parameter = df, method = METHOD)
    }

SCov.test <- function(X,location, n, p)
    {
    if (location=="est") T <- spatial.sign(X,center=TRUE,shape=FALSE) else T <- spatial.sign(X,center=FALSE,shape=FALSE)
    vSCOV <- as.vector(crossprod(T)/n)
    cpp<- Cpp(p)
    Tau <- (2 / (p*(p+2))) 
    Q2 <- sum((cpp %*% vSCOV)^2)
    test.statistic <- n*Q2/Tau
    df <- (p+2)*(p-1)/2
    p.value <- 1-pchisq(test.statistic, df)
    names(df)<-"df"
    names(test.statistic) <- "Q2"
    METHOD<-"Test for sphericity based on UCOV"
    list(statistic=test.statistic, p.value = p.value, parameter = df, method = METHOD)
    }