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March, 1987 Standardized Log-Likelihood Ratio Statistics for Mixtures of Discrete and Continuous Observations
J. L. Jensen
Ann. Statist. 15(1): 314-324 (March, 1987). DOI: 10.1214/aos/1176350268

Abstract

When the $\log$-likelihood statistic is divided by its mean, or an approximation to its mean, the limiting chi-squared distribution is often correct to order $n^{-3/2}$. Similarly, when the signed version of the likelihood ratio statistic is standardized with respect to its mean and variance the normal approximation is correct to order $n^{-3/2}$. Proofs for these statements have been given in great generality in the literature for the case of continuous observations. In this paper we consider cases where the minimal sufficient statistic is partly discrete and partly continuous. In particular, we consider testing problems associated with censored exponential life times.

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J. L. Jensen. "Standardized Log-Likelihood Ratio Statistics for Mixtures of Discrete and Continuous Observations." Ann. Statist. 15 (1) 314 - 324, March, 1987. https://doi.org/10.1214/aos/1176350268

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0613.62014
MathSciNet: MR885739
Digital Object Identifier: 10.1214/aos/1176350268

Subjects:
Primary: 62E20
Secondary: 62F05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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