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On large deviation expansion of distribution of maximum likelihood estimator and its application in large sample estimation
Authors:J C Fu  Gang Li and D L C Zhao
Institution:(1) Department of Statistics, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada;(2) Department of Math. Sciences, SUNY at Binghamton, 13902 Binghamton, NY, U.S.A.;(3) Department of Mathematics, Univ. of Science and Technology of China, Hefie, Anhui, China
Abstract:For estimating an unknown parameter theta, the likelihood principle yields the maximum likelihood estimator. It is often favoured especially by the applied statistician, for its good properties in the large sample case. In this paper, a large deviation expansion for the distribution of the maximum likelihood estimator is obtained. The asymptotic expansion provides a useful tool to approximate the tail probability of the maximum likelihood estimator and to make statistical inference. Theoretical and numerical examples are given. Numerical results show that the large deviation approximation performs much better than the classical normal approximation.This work is supported in part by the Natural Science and Engineering Research Council of Canada under grant NSERC A-9216.This author is also partially supported by the National Science Foundation of China.
Keywords:Large deviation expansion  maximum likelihood estimator  exponential rate
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