Nothing
ST <- function(X.f, Y.f, sub.size, test.set, M=500, alpha=0.05) {
n <- dim(X.f)[1]
p <- dim(X.f)[2]
n1 <- sub.size
n0 <- n-floor(n1)
S1 <- sample(1:n, floor(n1), replace=FALSE)
X.sub <- X.f[S1,]
Y.sub <- Y.f[S1]
cvfit <- cv.glmnet(X.sub, Y.sub, intercept=FALSE)
cf <- as.numeric(coef(cvfit, s="lambda.min"))[-1]
set1 <- (1:p)[abs(cf)>0]
resi <- Y.sub-X.sub%*%cf
beta.m <- t(standardize(X.sub[,-set1]))%*%resi
screen.set <- sort(order(abs(beta.m),decreasing=TRUE)[1:(n0-1-length(set1))])
a <- (1:p)[-set1]
screen.set <- union(a[screen.set],set1)
X <- X.f[-S1,screen.set]
Y <- Y.f[-S1]
score.nodewiselasso = getFromNamespace("score.nodewiselasso", "hdi")
node <- score.nodewiselasso(X, wantTheta=TRUE, verbose=FALSE, lambdaseq="quantile",
parallel=FALSE, ncores=2, oldschool = FALSE, lambdatuningfactor = 1)
Theta <- node$out
Gram<-t(X)%*%X/n0
sreg <- scalreg(X,Y)
beta.hat <- sreg$coefficients
sigma.sq <- sum((Y-X%*%beta.hat)^2)/(n0-sum(abs(beta.hat)>0))
test.set.i <- intersect(screen.set,test.set)
index <- screen.set%in%test.set.i
Omega <- diag(Theta%*%Gram%*%t(Theta))*sigma.sq
beta.db <- beta.hat+Theta%*%t(X)%*%(Y-X%*%beta.hat)/n0
margin.st <- sqrt(n0)*abs(beta.db[index])/sqrt(Omega[index])
margin.nst <- sqrt(n0)*abs(beta.db[index])
stat.st <- max(margin.st)
stat.nst <- max(margin.nst)
stat.boot.st <- stat.boot.nst <- rep(NA,M)
for (i in 1:M) {
e <- rnorm(n0)
xi.boot <- Theta[index,]%*%t(X)%*%e*sqrt(sigma.sq)/sqrt(n0)
stat.boot.nst[i] <- max(abs(xi.boot))
stat.boot.st[i] <- max(abs(xi.boot/sqrt(Omega[index])))
}
if (stat.nst>quantile(stat.boot.nst,1-alpha)) rej.nst <- "reject" else rej.nst <- "fail to reject"
if (stat.st>quantile(stat.boot.st,1-alpha)) rej.st <- "rejct" else rej.st <- "fail to reject"
result <- list(stat.nst, rej.nst, stat.st, rej.st)
names(result) <- c("non-studentized test","non-studentized test","studentized test","studentized test")
return(result)
}
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