Robust estimators based on generalization of trimmed mean

ABSTRACT

In this article, we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it, and compute the (iterative) weighted mean from it. By doing so, we obtain a robust estimator in the sense of the breakdown point, which uses more observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector space and allow multi-valued estimators.

KEYWORDS:

• Breakdown point
• Estimators
• Geometric median
• Location
• Trimmed mean

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G35
• 62G05

Acknowledgment

The authors would like to thank anonymous reviewers for substantially improving this article.