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September, 1982 Large Sample Point Estimation: A Large Deviation Theory Approach
James C. Fu
Ann. Statist. 10(3): 762-771 (September, 1982). DOI: 10.1214/aos/1176345869


In this paper the exponential rates of decrease and bounds on tail probabilities for consistent estimators are studied using large deviation methods. The asymptotic expansions of Bahadur bounds and exponential rates in the case of the maximum likelihood estimator are obtained. Based on these results we have obtained a result parallel to the Fisher-Rao-Efron result concerning second-order efficiency (see Efron, 1975). Our results also substantiate the geometric observation given by Efron (1975) that if the statistical curvature of the underlying distribution is small, then the maximum likelihood estimator is nearly optimal.


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James C. Fu. "Large Sample Point Estimation: A Large Deviation Theory Approach." Ann. Statist. 10 (3) 762 - 771, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62031
MathSciNet: MR663430
Digital Object Identifier: 10.1214/aos/1176345869

Primary: 62E20
Secondary: 62E10

Keywords: Bahadur bound , consistent estimator , exponential rate of convergence , maximum likelihood estimator , probability of large deviation , second-order efficiency , statistical curvature

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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