Question: Variance estimation with post stratification. Suppose we post stratify the sample into L post strata, with population counts N1, N2. . . NL. Then the

Variance estimation with post stratification. Suppose we post stratify the sample into L post strata, with population counts N1, N2. . . NL. Then the post stratified estimator for the population total is

Variance estimation with post stratification. Suppose we post stratify the sample into

Where

L post strata, with population counts N1, N2. . . NL. Then

And xli =1 if unit i is in post stratum l and 0 otherwise. Show, using linearization, that

the post stratified estimator for the population total isWhereAnd xli =1 if

We can thus let

unit i is in post stratum l and 0 otherwise. Show, using

and estimate V(ṫpost) by

linearization, thatWe can thus letand estimate V(ṫpost) by

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