Robust regression based on infinitesimal neighbourhoods. (English) Zbl 0567.62051

Bickel, P. J.

Ann. Stat. 12, 1349-1368 (1984).

Robust estimation in the general normal regression model with carriers permitting small departures from the model is studied. The solutions obtained contain as special case the solutions of P. J. Huber [J. Am. Stat. Assoc. 78, 66-80 (1983; Zbl 0514.62073)] and W. S. Krasker and R. E. Welsch [ibid. 77, 595-604 (1982; Zbl 0501.62062)] and give also some new procedures. The calculations indicate that the optimality properties of these estimates are more limited than suggested by Krasker and Welsch.

Reviewer: M.Huškova

MSC:

62J05	Linear regression; mixed models
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

infinitesimal neighbourhoods; Robust estimation; general normal regression model

Citations:

Zbl 0514.62073; Zbl 0501.62062