The problem of dimensionality in stratified sampling

The problem of dimensionality in stratified sampling

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Article ID: iaor19911792
Country: United States
Volume: 35
Issue: 11
Start Page Number: 1278
End Page Number: 1296
Publication Date: Nov 1989
Journal: Management Science
Authors: ,
Keywords: statistics: sampling
Abstract:

Stratified sampling is perhaps the most natural of the variance reduction techniques. However its use is often frustrated by the high dimensionality of the sample space. This paper investigates the difficulty and suggests a basic sampling scheme for use in such problems. The accuracy of estimators when this method of sampling is used is examined in detail. A way of implementing the scheme in practice is suggested which makes use of shadow response variables (variables which have similar properties to control variables). This reduces the dimensionality of the sample space to a tractable size. Two detailed examples are given for which a 10% to 90% reduction in variance is obtained compared with crude Monte Carlo.

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