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Comment.

Authors :
Bickel, Peter J.
Source :
Journal of the American Statistical Association. Mar1983, Vol. 78 Issue 381, p75. 3p.
Publication Year :
1983

Abstract

The author here comments on the research paper by Peter J. Huber, related to the minimax aspects of the bounded-influence regression. In his opinion Huber's paper is a major contribution to robust regression, clarifying the relationships among the various methods that have been proposed. The author here put the asymptotic case in the framework of infinitesimal neighborhood models and use the technique of statistician H. Rieder to rederive the formulas presented in the paper and extend them to the full p-variate case. The asymptotic minimax results in the univariate case are seen to be valid for general loss functions rather than only for Huber's testing-related measure. The relation to errors-in-variables models becomes clear. The author remarks that the p-variate extension suggests that more complicated estimates that choose an appropriate coordinate system in the X space before clipping may improve the solution of a particular section in the paper. The author presents all the formulae and calculations needed to prove his point.

Details

Language :
English
ISSN :
01621459
Volume :
78
Issue :
381
Database :
Academic Search Index
Journal :
Journal of the American Statistical Association
Publication Type :
Academic Journal
Accession number :
4607739
Full Text :
https://doi.org/10.1080/01621459.1983.10477931