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Summary: Bahadur efficiency of the likelihood ratio test
Miguel A. Arcones
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 13902. USA.
E-mail: arcones@math.binghamton.edu.
June 6, 2005
Abstract
We present a new approach to study the Bahadur efficiency of likelihood tests. Our
approach is based on the large deviation principle for empirical processes. We prove
that the likelihood ratio test is Bahadur asymptotically optimal under mild sufficient
conditions. Our results apply to common families of distributions such as location and
scale families.
Running Title: likelihood ratio tests
1 Introduction
A natural definition of efficiency of tests was given by Bahadur (1965, 1967, 1971). This
definition is as follows. Let {f(·, ) : } be a family of pdf's on a measurable space (S, S)
with respect to a measure µ, where is a Borel subset of Rd
. Let X1, . . . , Xn be i.i.d.r.v.'s
with values in (S, S) and pdf f(·, ), for some unkonwn value of . Let 0 . Consider
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