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A simple variance estimator for unequal probability sampling without replacement

Berger, Yves G. (2003) A simple variance estimator for unequal probability sampling without replacement , Southampton, GB University of Southampton 14pp. (S3RI Methodology Working Papers, M03/09).

Record type: Monograph (Working Paper)

Abstract

Survey sampling textbooks often refer to the Sen-Yates-Grundy variance estimator for use with without replacement unequal probability designs. This estimator is rarely implemented, because of the complexity of determining joint inclusion probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen-Hurwitz with replacement variance estimator; which often leads to overestimation of the variance for large sampling fraction that are common in business surveys. We will consider an alternative estimator: the Hájek (1964) variance estimator that depends on the first-order inclusion probabilities only and is usually more accurate than the Hansen-Hurwitz estimator. We review this estimator and show its practical value. We propose a simple alternative expression; which is as simple as the Hansen-Hurwitz estimator. We also show how the Hájek estimator can be easily implemented with standard statistical packages.

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Published date: 20 May 2003

Identifiers

Local EPrints ID: 7798
URI: http://eprints.soton.ac.uk/id/eprint/7798
PURE UUID: 869fa83b-1a89-42d5-a57f-cc7995317243

Catalogue record

Date deposited: 09 Jun 2004
Last modified: 17 Jul 2017 17:14

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