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

Where

Variance estimation with post stratification. Suppose we post stratify the

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

Variance estimation with post stratification. Suppose we post stratify the

We can thus let

Variance estimation with post stratification. Suppose we post stratify the

and estimate V(ṫpost) by

Variance estimation with post stratification. Suppose we post stratify the

Ni ; l-I l=2.wixliyi, Ni= ies 1-1

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