Optimal robust estimates using the Hellinger distance

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State: Public
Version: author
Serval ID
serval:BIB_53BD96FE77EA
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Optimal robust estimates using the Hellinger distance
Journal
Advances in Data Analysis and Classification
Author(s)
Marazzi Alfio, Yohai Victor J.
ISSN
1862-5347
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
4
Number
2-3
Pages
169-179
Language
english
Abstract
Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance.We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too.We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates.
Create date
30/11/2010 17:44
Last modification date
20/08/2019 15:08
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