A method of determining the winsorization threshold, with an application to domain estimation

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Cyril Favre Martinoz, David Haziza and Jean-François Beaumont^Note 1

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Abstract

In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.

Key Words: Conditional bias; Robust estimation; Winsorized estimator; Influential values.

Table of content

• 1. Introduction
• 2. Measure of influence: Conditional bias
• 3. Robust estimation based on the conditional bias
• 4. Application to winsorized estimators
• 5. Robust estimation of domain totals
• 6. Simulation studies
• 7. Discussion
• Acknowledgements
• Appendix
• References

Notes