The Problem of Dimensionality in Stratified Sampling

Russell C. H. Cheng and Teresa Davenport
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Russell C. H. Cheng: Department of Mathematics, UWIST, Cardiff, United Kingdom
Teresa Davenport: Department of Mathematics, UWIST, Cardiff, United Kingdom

Management Science, 1989, vol. 35, issue 11, 1278-1296

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.

Keywords: control variables; quasirandom sequences; stratified sampling; shadow response; variance reduction (search for similar items in EconPapers)
Date: 1989
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