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December, 1984 A Large Deviation Result for the Likelihood Ratio Statistic in Exponential Families
Stavros Kourouklis
Ann. Statist. 12(4): 1510-1521 (December, 1984). DOI: 10.1214/aos/1176346807

Abstract

In this paper we consider exponential families of distributions and obtain under certain conditions a uniform large deviation result about the tail probability $P_\partial(\phi_\partial(\bar{X}_n) > \varepsilon), \varepsilon > 0$, where $\partial$ is the natural parameter and $\phi_\partial(\bar{X}_n)$ is the $\log$ likelihood ratio statistic for testing the null hypothesis $\{\partial\}$. The technique involves approximating certain convex compact sets in $R^k$ by polytopes, then estimating the probability contents of associated closed halfspaces, and counting the number of these half-spaces. Some examples are given, among them the multivariate normal distribution with unknown mean vector and covariance matrix.

Citation

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Stavros Kourouklis. "A Large Deviation Result for the Likelihood Ratio Statistic in Exponential Families." Ann. Statist. 12 (4) 1510 - 1521, December, 1984. https://doi.org/10.1214/aos/1176346807

Information

Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0551.62017
MathSciNet: MR760703
Digital Object Identifier: 10.1214/aos/1176346807

Subjects:
Primary: 60F10
Secondary: 52A20, 52A25, 62F03

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 4 • December, 1984
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