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

Cyril Favre-Martinoz (1, 2) , David Haziza (3, 2) , Jean-François Beaumont (4, 5)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CREST - Centre de Recherche en Economie et Statistique [Bruz]
3 UdeM - Université de Montréal
4 Statistics Canada
5 Statistical Research and Innovation Division

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.

Mots clés: conditional bias; robust estimation; Winsorized estimator; influential values

Domaines: Statistiques [math.ST]

Cyril Favre-Martinoz, David Haziza, Jean-François Beaumont. A method of determining the winsorization threshold, with an application to domain estimation. Survey Methodology, 2015, 41 (1), pp.57-77. ⟨hal-01252343⟩