Summary: Moderate deviations for Mestimators
Miguel A. Arcones
Department of Mathematical Sciences
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.
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).