On the speed of convergence in the central limit theorem of log-likelihood ratio processes |
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Authors: | A K Basu D Bhattacharya |
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Institution: | (1) Department of Statistics, Calcutta University, India;(2) Department of Mathematics, Visva-Bharati University, India |
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Abstract: | Let
, the parameter space, be an open subset ofR
k
,k 1. For each
, let the r.v.'sX
n
,n=1, 2,... be defined on the probability space (X, P
) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the -field of Borel subsets ofS. Forh R
k
and a sequence of p.d. normalizing matrices
n
=
n
k × k
( 0 set
n
*
= * = 0 +
n
h, where 0 is the true value of , such that *,
. Let
n
( *, *)( be the log-likelihood ratio of the probability measure
with respect to the probability measure
, whereP
n
is the restriction ofP
over
n
= (X
1,X
2,...,X
n
. In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account. |
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Keywords: | Speed of convergence CLT log-likelihood ratio process |
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