Winsorization methods in sample surveys

Abstract

This thesis covers winsorization-based outlier-robust estimators for sample surveys. In this field, the aim is to predict the total of a finite population of values, from a with replacement sample. While many mainstream outlier methods can be applied to surveys, there are several issues peculiar to finite population estimation. For instance, there is a strong distinction between true and untrue/unrepresentative outliers. Untrue outliers, for example due to miscoding, should be excluded from estimation. However, it is crucial to retain large but true outliers in some form, as they are likely to reflect other large values in the population. This thesis is concerned only with true outliers; other cases belong to the field of editing.

Large sample sizes are another feature of many sample survey applications. For instance, official economic surveys often include many thousands of units, so estimators may have very low bias. If an outlier method introduces even a small bias, the bias can dominate the mean squared error. Because of this it is crucial to apply outlier methods carefully, otherwise the estimator may be made much less efficient than non-robust methods. Section 3 discusses choice of parameters in one outlier-robust estimator, the winsorized ratio estimator, in order to ensure that the mean squared error is improved by the method.

Section 2 contains a selected review of outlier-robust sample survey estimators, with particular emphasis on winsorized estimators. In Section 3, I derive cutoffs to minimise the mean squared error of the winsorized ratio estimator. The optimal cutoffs are shown to satisfy a surprisingly simple and general property. Section 4 describes a simulation study undertaken to evaluate the winsorized ratio estimator. Section 5 contains conclusions. Show more