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Asymptotic consistency under large entropy sampling designs with unequal probabilities

Asymptotic consistency under large entropy sampling designs with unequal probabilities
Asymptotic consistency under large entropy sampling designs with unequal probabilities
A large part of survey sampling literature is devoted to unequal probabilities sampling designs without replacement. Brewer and Hanif (1983) provided a summary of these sampling designs. The maximum entropy designs is one of them. Consistency results have been proven for the maximum entropy sampling (Hájek, 1964). The aim is to give sufficient conditions under which Hájek (1964) consistency results still hold for large entropy sampling designs which are different from the maximum entropy design. These conditions involve modes of convergence of sampling designs towards the maximum entropy design. We show that these conditions are satisfied for the popular Rao-Sampford (Rao, 1965, Sampford, 1967) design. Our consistency results are applied to the Hájek (1964) simple variance estimator. This estimator does not require joint-inclusion probabilities and can be easily estimated using weighted least squares regression (Berger, 2004, 2005b). Deville (1999) conjectured that this estimator is suitable for any sampling designs (see also Brewer and Donadio, 2003). Our consistency result gives regularity conditions under which this estimator is consistent which justifies Deville’s (1999) conjecture.
1012-9367
407-426
Berger, Yves G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b
Berger, Yves G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b

Berger, Yves G. (2011) Asymptotic consistency under large entropy sampling designs with unequal probabilities. Pakistan Journal of Statistics, 27 (4), 407-426.

Record type: Article

Abstract

A large part of survey sampling literature is devoted to unequal probabilities sampling designs without replacement. Brewer and Hanif (1983) provided a summary of these sampling designs. The maximum entropy designs is one of them. Consistency results have been proven for the maximum entropy sampling (Hájek, 1964). The aim is to give sufficient conditions under which Hájek (1964) consistency results still hold for large entropy sampling designs which are different from the maximum entropy design. These conditions involve modes of convergence of sampling designs towards the maximum entropy design. We show that these conditions are satisfied for the popular Rao-Sampford (Rao, 1965, Sampford, 1967) design. Our consistency results are applied to the Hájek (1964) simple variance estimator. This estimator does not require joint-inclusion probabilities and can be easily estimated using weighted least squares regression (Berger, 2004, 2005b). Deville (1999) conjectured that this estimator is suitable for any sampling designs (see also Brewer and Donadio, 2003). Our consistency result gives regularity conditions under which this estimator is consistent which justifies Deville’s (1999) conjecture.

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Published date: October 2011
Organisations: Statistical Sciences Research Institute

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Local EPrints ID: 350396
URI: https://eprints.soton.ac.uk/id/eprint/350396
ISSN: 1012-9367
PURE UUID: 706dce5e-001b-48f6-b3de-54109a114478

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Date deposited: 27 Mar 2013 11:52
Last modified: 18 Jul 2017 04:35

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