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October 2007 Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models
Heping He, Thomas A. Severini
Ann. Statist. 35(5): 2054-2074 (October 2007). DOI: 10.1214/009053607000000307

Abstract

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n−1, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as (θ̂, a), where θ̂ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order n−1 without making any assumption about the sufficient statistic of the model.

Citation

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Heping He. Thomas A. Severini. "Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models." Ann. Statist. 35 (5) 2054 - 2074, October 2007. https://doi.org/10.1214/009053607000000307

Information

Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62013
MathSciNet: MR2363963
Digital Object Identifier: 10.1214/009053607000000307

Subjects:
Primary: 62F05
Secondary: 62F03

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • October 2007
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