On the Choice of Tuning Constants for Winsorized Estimators

• Activity Number: 365
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): David Haziza*+ and Cyril Favre-Martinoz and Jean-Francois Beaumont
• Companies: Université de Montréal and CREST/ENSAI and Statistics Canada
• Keywords: influential unit ; winsorization ; conditional bias ; calibration

Abstract

Influential units occur in business surveys because the distributions of economic variables tend to be highly skewed. In the presence of influential units, classical estimators (e.g., Horvitz-Thompson estimator) exhibit larges variances. Winsorization (Type I and Type II) is often used in business surveys in order to obtain more stable estimates. The winsorized estimators involve a tuning constant. We propose a simple method for determining the tuning constant, which consists of minimizing the maximum estimated conditional bias. We show that the resulting estimator is consistent. In the case of stratified simple random sampling, winsorization is typically applied independently within each stratum. However, the resulting estimator of the overall total may be considerably biased. To overcome this difficulty, we propose a method, where winsorized estimators within each stratum are modified so that their sum is calibrated on the winsorized estimator obtained independently at the overall level. Results of a simulation study will be presented.