Title
Stahel-Donoho estimators with cellwise weights Stahel-Donoho estimators with cellwise weights
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
London ,
Subject
Mathematics
Computer. Automation
Source (journal)
Journal of statistical computation and simulation. - London
Volume/pages
81(2011) :1 , p. 1-27
ISSN
0094-9655
ISI
000285347900001
Carrier
E
Target language
Dutch (dut)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The Stahel-Donoho estimator is defined as a weighted mean and covariance, where each observation receives a weight which depends on a measure of its outlyingness. Therefore, all variables are treated in the same way whether they are responsible for the outlyingness or not. We present an adaptation of the Stahel-Donoho estimator, where we allow separate weights for each variable. By using cellwise weights, we aim to only downweight the contaminated variables such that we avoid losing the information contained in the other variables. The goal is to increase the precision and possibly the robustness, of the estimator. We compare several variants of our proposal and show to what extent they succeed in identifying and downweighting precisely those variables which are contaminated. We further demonstrate that in many situations the mean-squared error of the adapted estimators is lower than that of the original Stahel-Donoho estimator and that this results in better outlier detection capabilities. We also consider some real data examples.
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