Variance reduction and nonnormality

Abstract

There are many available variance reduction methods and these are described in the sampling theory literature in such works as Kish (1965) and Raj (1968), and in the literature of Monte Carlo methods (Hammersley & Handscomb, 1964) and in the survey paper by Halton (1970). In sampling problems where a mean is to be estimated, these variance reduction methods may induce extreme nonnormality in the distribution of the resulting estimate which in turn may cause difficulties with assessment of the error of the estimate and with other inferential procedures. We have emphasized the effects on ,81 = 2/(J6 of four major techniques of variance reduction, namely, importance or probability proportional to estimated size sampling, regression, the use of conditional expectation, and stratification. The results are readily extended to include the effects on ,82 = ,04/o-4. To facilitate comparisons with population values, (J2 and ft1 are expressed on a unit observation basis throughout.