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## discoveries for standardized data
discoveries = function(y, X, xs, hyps, maxit=0, alpha=0.05){
rh = actgt(y,X,xs,hyps,maxit=maxit,alpha=alpha)[1]
if(rh == "not reject" ){
dis=0
} else if(rh=="unsure"){
dis = "unsure"
} else{
sqrW = sqrt(mean(y)*(1-mean(y)) ) # sqrt of covariance of y
WIHZ = sqrW *(sweep(X,2,colMeans(X))) ## W^{1/2}*(I-H)Z
IHZ = WIHZ/sqrW ##(I-H)Z
itest = sapply(hyps, function(i) sum(colSums(y*IHZ[,i,drop=FALSE])^2))
candidates = names(sort(itest))
if(length(candidates)==1){
dis=1
} else{
for(i in (length(candidates)-1):1){
rc = actgt(y=y, X=X, xs=xs,hyps = candidates[1:i],maxit=maxit,alpha=alpha)
if(rc[1]=="not reject" || rc[1]=="unsure"){
dis = length(candidates)-i
break
}
if(i==1 && rc[1]=="reject"){
dis = length(candidates)-i
}
}
}
}
return(dis)
}
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