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dfs_pick<-function(xtab, ytab, x, k, rho, ci = TRUE){
# conditions
stopifnot(length(xtab)==length(ytab))
if(length(rho)==1) rho <- rep(rho,length(x))
stopifnot(length(rho)==length(x))
if(length(k)==1) k <- rep(k,length(x))
stopifnot(length(k)==length(x))
# initialization
n = length(xtab)
nx = length(x)
res = rep(0, nx)
lowCI_phitilde = rep(0, nx)
upCI_phitilde = rep(0, nx)
for (j in 1:nx){
# value of interest:
xj = x[j]
# Transformed data (z=column vector):
z = ytab * as.numeric(xtab <= xj)
zsort = sort(z)
kx=floor((length(which(z>0)))^0.5)- k[j] + 1
gk1 = zsort[n-kx+1]
gk2 = zsort[n-2*kx+1]
evi = rho[j]
var3 = (evi^(-2))*(2^(-2/evi))/((2^(-1/evi) -1)^4)
res[j] = gk1 + (gk1-gk2)/(2^(1/evi)-1)
lowCI_phitilde[j] = res[j] -1.96*sqrt(var3/(2*kx))*(gk1-gk2)
upCI_phitilde[j] = res[j] +1.96*sqrt(var3/(2*kx))*(gk1-gk2)
}
if(ci)
res<-cbind(res, lowCI_phitilde, upCI_phitilde)
return(res)
}
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