Estimator of Horvitz-Thompson VarianceWhat is the estimator o... | Filo
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3. Horvitz-Thompson EstimatorRecall the HT estimator ishatmuHT = frac1n sumi in S fracXipii,where pii is the inclusion probability for Xi, S is the sample, and n is the size of population.1. Define piij to be the probability that Xi and Xj are both in the sample S, with piij = piifor convenience when i = j. Show thatVar(hatmuHT) = frac1n^2 sumi=1^n sumj=1^n Xi Xj (fracpiijpii pij - 1).2. With the sample data, we give an estimation of the variance, ashatV = frac1n^2 sumi in S sumj in S Xi Xj (fra
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