The Annals of Statistics

Robust Regression Based on Infinitesimal Neighbourhoods

P. J. Bickel

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1349-1368.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346796

Digital Object Identifier
doi:10.1214/aos/1176346796

Mathematical Reviews number (MathSciNet)
MR760693

Zentralblatt MATH identifier
0567.62051

JSTOR
links.jstor.org

Subjects
Primary: 62J05: Linear regression
Secondary: 62F35: Robustness and adaptive procedures

Keywords
Regression robustness infinitesimal neighbourhoods Krasker-Welsch estimates

Citation

Bickel, P. J. Robust Regression Based on Infinitesimal Neighbourhoods. Ann. Statist. 12 (1984), no. 4, 1349--1368. doi:10.1214/aos/1176346796. https://projecteuclid.org/euclid.aos/1176346796


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