Large Sample Point Estimation: A Large Deviation Theory Approach
The Annals of Statistics · 1982 · Volume 10 · Issue 3
Abstract
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.
Keywords
62E10, 62E20, Bahadur bound, consistent estimator, exponential rate of convergence, maximum likelihood estimator, probability of large deviation, second-order efficiency, statistical curvature
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