Open Access
December, 1984 Robust Regression Based on Infinitesimal Neighbourhoods
P. J. Bickel
Ann. Statist. 12(4): 1349-1368 (December, 1984). DOI: 10.1214/aos/1176346796


We study robust estimation in the general normal regression model with random carriers permitting small departures from the model. The framework is that of Bickel (1981). We obtain solutions of Huber (1982), Krasker-Hampel (1980) and Krasker-Welsch (1982) as special cases as well as some new procedures. Our calculations indicate that the optimality properties of these estimates are more limited than suggested by Krasker and Welsch.


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P. J. Bickel. "Robust Regression Based on Infinitesimal Neighbourhoods." Ann. Statist. 12 (4) 1349 - 1368, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0567.62051
MathSciNet: MR760693
Digital Object Identifier: 10.1214/aos/1176346796

Primary: 62J05
Secondary: 62F35

Keywords: infinitesimal neighbourhoods , Krasker-Welsch estimates , regression , robustness

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • December, 1984
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