JSM 2005 - Toronto

Abstract #303584

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 358
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #303584
Title: Elementary Chis Squared
Author(s): George Terrell*+
Companies: Virginia Polytechnic Institute and State University
Address: Statistics Department Virginia Tech, Blacksburg, VA, 24061, United States
Keywords: Chi square statistics ; Maximum likelihood ; Likelihood ratio statistic ; Score statistic ; Wald statistic ; Gradient statistic
Abstract:

When testing hypotheses in nonnormal parametric models, we most commonly use statistics that are asymptotically chi-squared distributed. Some general forms for these are the Wilks (1938) log-likelihood-ratio statistic, the Wald (1943) statistic, and the Rao (1947) score statistic. All are still in wide use, and a half century of study has not entirely resolved the relationships between them and their relative merits. We will show that, in a certain sense, there are precisely five general forms for asymptotically chi-squared statistics based on the likelihood function. This provides a new framework for investigating the question of which to use under what circumstance.

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