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ON LARGE DEVIATION EXPANSION OF DISTRIBUTION

OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS

APPLICATION IN LARGE SAMPLE ESTIMATION

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J. C. FU^{1}, GANG LI^{2} AND L. C. ZHAO^{3}

^{1} *Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2*

^{2} *Department of Math. Sciences, SUNY at Binghamton, Binghamton, NY 13902, U.S.A.*

^{3} *Department of Mathematics, Univ. of Science and Technology of China, Hefie, Anhui, China*
(Received April 10, 1991; revised September 29, 1992)

**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.

*Key words and phrases*:
Large deviation expansion, maximum
likelihood estimator, exponential rate.

**Source**
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