A simple variance estimator for unequal probability sampling without replacement

Berger, Yves G. (2004) A simple variance estimator for unequal probability sampling without replacement. Journal of Applied Statistics, 31, (3), 305-315. (doi:10.1080/0266476042000184046).


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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 fractions 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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1080/0266476042000184046
ISSNs: 0266-4763 (print)
Related URLs:
Keywords: design-based inference, hansen-hurwitz variance estimator, inclusion probabilities, &pgr, estimator, sen-yates-grundy Variance Estimator
Subjects: H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Social Sciences > Social Statistics
Faculty of Social and Human Sciences
ePrint ID: 34120
Accepted Date and Publication Date:
Date Deposited: 15 May 2006
Last Modified: 31 Mar 2016 12:01
URI: http://eprints.soton.ac.uk/id/eprint/34120

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