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Moderate deviations for Mestimators Miguel A. Arcones

Summary: Moderate deviations for M­estimators
Miguel A. Arcones
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 13902
April 11, 2002
We present general sufficient conditions for the moderate deviations of M­
estimators. These results are applied to many different types of M-estimators such
as the p­th quantile, the spatial median, the least absolute deviation estimator
in linear regression, maximum likelihood estimators and other location estimators.
We apply moderate deviations theorems from empirical processes.
Key Words: M­estimators, moderate deviations, maximum likelihood estima-
AMS subject classification: 60F10, 62E20.
1 Introduction
We discuss the moderate deviations for M­estimators. Huber (1964) in-
troduced M­estimators as a way to obtain more robust estimators. Let
i=1 be a sequence of i.i.d.r.v.'s with values in a measurable space (S, S).


Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton


Collections: Mathematics