Article

A Simple Variance Estimator for Unequal Probability Sampling without Replacement

Journal of Applied Statistics 01/2004; 31(3):305-315. pp.305-315
Source: RePEc

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 Hajek (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 Hajek estimator can be easily implemented with standard statistical packages.

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Keywords

alternative estimator
 
business surveys
 
estimator
 
first-order inclusion probabilities
 
Hajek estimator
 
Hansen- Hurwitz estimator
 
Hansen-Hurwitz
 
Hansen-Hurwitz estimator
 
joint inclusion probabilities
 
large sampling fractions
 
overestimation
 
practical value
 
replacement variance estimator
 
Sen-Yates-Grundy variance estimator
 
simpler variance estimators
 
standard statistical packages
 
Survey sampling textbooks
 
variance
 
without-replacement unequal probability designs