A simple variance estimator for unequal probability sampling without replacement
A simple variance estimator for unequal probability sampling without replacement
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.
design-based inference, hansen-hurwitz variance estimator, inclusion probabilities, &pgr, estimator, sen-yates-grundy Variance Estimator
305-315
Berger, Yves G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b
2004
Berger, Yves G.
8fd6af5c-31e6-4130-8b53-90910bf2f43b
Berger, Yves G.
(2004)
A simple variance estimator for unequal probability sampling without replacement.
Journal of Applied Statistics, 31 (3), .
(doi:10.1080/0266476042000184046).
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 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.
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More information
Published date: 2004
Keywords:
design-based inference, hansen-hurwitz variance estimator, inclusion probabilities, &pgr, estimator, sen-yates-grundy Variance Estimator
Organisations:
Faculty of Social, Human and Mathematical Sciences
Identifiers
Local EPrints ID: 34120
URI: http://eprints.soton.ac.uk/id/eprint/34120
ISSN: 0266-4763
PURE UUID: bc721b67-c0a0-40f0-929f-f10cca6b6b1c
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Date deposited: 15 May 2006
Last modified: 16 Mar 2024 03:03
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