The University of Southampton
University of Southampton Institutional Repository

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)


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.

PDF 7798-01.pdf - Other
Download (145kB)

More information

Published date: 20 May 2003


Local EPrints ID: 7798
PURE UUID: 869fa83b-1a89-42d5-a57f-cc7995317243

Catalogue record

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

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.