Minimum distance estimation in multiple linear regression. (English) Zbl 0607.62038

The author describes a class of minimum distance Cramér-von Mises type estimators of the parameter vector in the multiple linear regression model, in terms of weighted empiricals. He has shown that the estimators corresponding to the weights proportional to the design matrix are asymptotically efficient within the class at a given error distribution. The paper also deals with the qualitative robustness of these estimators under heteroscedastic gross errors and heteroscedastic scale errors.
Reviewer: N.Mohanty


62G05 Nonparametric estimation
62J05 Linear regression; mixed models
62F35 Robustness and adaptive procedures (parametric inference)
62G20 Asymptotic properties of nonparametric inference