#' @export
E.STpiPS<-function(y,pik,S){
S<-as.factor(S)
y<-cbind(1,y)
y<-as.data.frame(y)
names(y)[1] <- "N"
pik<-as.data.frame(pik)
nh <- c(table(S))
Strata<-array(NA,c(4,length(nh)+1,dim(y)[2]))
rownames(Strata)=c("Estimation", "Standard Error","CVE","DEFF")
colnames(Strata)<-c(levels(S),"Population")
dimnames(Strata)[[3]]<-names(y)
S<-as.factor(as.integer(S))
for(k in 1: length(nh)){
nhe <- nh[k]
e<-which(S==k)
ye<-y[e,]
pike<-pik[e,]
ye<-as.matrix(ye)
tye<-matrix(1,1,dim(ye)[1])%*%(ye/pike)
#-------------------
ck <- (1-pike)*(nhe/(nhe-1))
P1 <- as.matrix(colSums(ck*ye/pike))
P2 <- sum(ck)
ystar <- t(P1%*%t(pike/P2))
P3 <- ck/(pike^2)
#--------------------
Vtye<-colSums(P3*((ye-ystar)^2))
CVe<-100*sqrt(Vtye)/tye
Nhe<-sum(1/pike)
VMAS<-as.vector((Nhe^2)*(1-(nhe/Nhe))*diag(var(ye))/(nhe))
DEFF<-Vtye/VMAS
Strata[1,,][k,]<-tye
Strata[2,,][k,]<-sqrt(Vtye)
Strata[3,,][k,]<-CVe
Strata[4,,][k,]<-DEFF
}
for(i in 1:dim(y)[2]){
Strata[1,,][(length(nh)+1),][i]<-sum(Strata[,,i][1,][1:length(nh)])
Strata[2,,][(length(nh)+1),][i]<-sqrt(sum(Strata[,,i][2,][1:length(nh)]))
Strata[3,,][(length(nh)+1),][i]<-100*sqrt(Strata[2,,][(length(nh)+1),][i])/Strata[1,,][(length(nh)+1),][i]
N <- sum(1/pik)
n <- sum(nh)
VMAST<-(N^2)*(1-(n/N))*var(y[,i])/(n)
Strata[4,,][(length(nh)+1),][i]<-(Strata[2,,][(length(nh)+1),][i])/(VMAST)
}
return(Strata)
}
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