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# Helper function to compute postStrat total for bootstrapping
postStratt <- function(data, xpoptab, indices){
# Define variables
x= N_h = N_h_hats = ps_h = poptotal_h = strat_pop_total = NULL
# data: 4th column: y_den, 3rd column:y_num,
# 2nd column:pis, 1st column: xsample
d <- data[indices,]
#y
y <- d[,3]
#pis
pis <- d[,2]
#xsample
xsample <- d[, 1]
#Estimator
#Compute estimator
dat <- data.frame(x=xsample, pi=pis,y=y)
tab <- dat |>
group_by(x) |>
summarize(poptotal_h = y%*%pi^(-1),N_h_hats = sum(pi^(-1)), var_h = var(y)) |>
inner_join(xpoptab, by=c("x")) |>
mutate(ps_h = N_h/N_h_hats, strat_pop_total = ps_h*poptotal_h, strat_pop_mean = strat_pop_total/N_h)
#calculating the total estimate for y
out <- sum(tab$strat_pop_total)
return(out)
}
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