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Asymptotic testing theory for generalized linear models

 

作者: L. Fahrmeir,  

 

期刊: Statistics  (Taylor Available online 1987)
卷期: Volume 18, issue 1  

页码: 65-76

 

ISSN:0233-1888

 

年代: 1987

 

DOI:10.1080/02331888708801992

 

出版商: Akademie-Verlag

 

关键词: Primary 62 F 05;secondary 62 H 15;Generalized linear models;hypothesis testing;likelihood ration statistic;score statistic;WALD statistic;asymptotic properties of tests

 

数据来源: Taylor

 

摘要:

Statistical inference in generalized linear models is based on the premises that the maximum likelihood estimator of unknown parameters is consistent and asymptotically normal, and that various test statistics have a limiting x2-distribution. FAHRMEIR and KAUFMANN (1985) present mild conditions which assure consistency and asymptotic normality of the maximum likelihood estimator. In this paper it is shown that under essentially tha same conditions the likelihood ration statistic, the Wald statistics and the score statistic are asymptotically equivalent, i.e. they have the same limiting x2-distributions under the general linear hypothesis as well as under suitable sequences of alternatives. Thus, statistical inference in generalized linear models is asymptotically justified under rather weak requirements.

 

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