The high entropy variance of the Horvitz-Thompson estimator - ARCHIVED

Using both purely design based and model assisted arguments, it is shown that, under conditions of high entropy, the variance of the Horvitz Thompson (HT) estimator depends almost entirely on first order inclusion probabilities. Approximate expressions and estimators are derived for this "high entropy" variance of the HT estimator. Monte Carlo simulation studies are conducted to examine the statistical properties of the proposed variance estimators.