On the convergence of the Horvitz-Thompson estimator

Robinson, Peter (1982) On the convergence of the Horvitz-Thompson estimator Australian Journal of Statistics, 24 (2). pp. 234-238. ISSN 0004-9581
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We investigate the degree to which the Horvitz-Thompson estimator approximates the population mean in survey sampling. Specifically, conditions for (mean square) consistency are given, along with rates of convergence. The conditions involve only first and second-order inclusion probabilities, and for various sampling designs they are easy to check.

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