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Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator

Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator
Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator
Drawing distinct units without replacement and with unequal probabilities from a population is a problem often considered in the literature (e.g. , Int. Statist. Rev. 48, 317-355). In such a case, the sample mean is a biased estimator of the population mean. For this reason, we use the unbiased Horvitz-Thompson estimator (1951). In this work, we focus our interest on the variance of this estimator. The variance is cumbersome to compute because it requires the calculation of a large number of second-order inclusion probabilities. It would be helpful to use an approximation that does not need heavy calculations. The a &unknown; jek (1964)> variance approximation provides this advantage as it is free of second-order inclusion probabilities. a &unknown; jek (1964)> proved that this approximation is valid under restrictive conditions that are usually not fulfilled in practice. In this paper, we give more general conditions and we show that this approximation remains acceptable for most practical problems.
0378-3758
149-168
Berger, Y.G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b
Berger, Y.G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b

Berger, Y.G. (1998) Rate of convergence for asymptotic variance of the Horvitz-Thompson estimator. Journal of Statistical Planning and Inference, 74 (1), 149-168. (doi:10.1016/S0378-3758(98)00107-4).

Record type: Article

Abstract

Drawing distinct units without replacement and with unequal probabilities from a population is a problem often considered in the literature (e.g. , Int. Statist. Rev. 48, 317-355). In such a case, the sample mean is a biased estimator of the population mean. For this reason, we use the unbiased Horvitz-Thompson estimator (1951). In this work, we focus our interest on the variance of this estimator. The variance is cumbersome to compute because it requires the calculation of a large number of second-order inclusion probabilities. It would be helpful to use an approximation that does not need heavy calculations. The a &unknown; jek (1964)> variance approximation provides this advantage as it is free of second-order inclusion probabilities. a &unknown; jek (1964)> proved that this approximation is valid under restrictive conditions that are usually not fulfilled in practice. In this paper, we give more general conditions and we show that this approximation remains acceptable for most practical problems.

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Published date: 1 October 1998

Identifiers

Local EPrints ID: 34116
URI: https://eprints.soton.ac.uk/id/eprint/34116
ISSN: 0378-3758
PURE UUID: 79e57837-5686-45af-9ce1-a7fe7b101386

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Date deposited: 11 Jan 2008
Last modified: 17 Jul 2017 15:51

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