On the Asymptotic Distribution of the Likelihood Ratio Statistic

Likelihood ratio tests are among the most frequently used in practical statistics. Important references on this subject include Wilks ( 1962 ), Rao ( 1965 , pp. 347-352), and Agresti ( 1990 , pp. 434-435). We give proofs of some well-known results on the limiting distribution of D = −2log(λ), where...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 36; no. 2; pp. 273 - 281
Main Author Scott, W. F.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 06.02.2007
Taylor & Francis
Subjects
Contingency tables
Distribution theory
Exact sciences and technology
Fisher's information
General topics
Limit theorems
Mathematics
Maximum likelihood estimation
Multivariate analysis
Primary 62F09
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Secondary 62P25
Statistics
Statistical method
Maximum likelihood estimation
Limit distribution
Likelihood ratio test
Secondary 62P25
Primary 62F09
Likelihood ratio
Contingency table
Maximum likelihood
Fisher's information
Fisher information
Contingency tables
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ISSN0361-0926
1532-415X
DOI10.1080/03610920600974229

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Summary:Likelihood ratio tests are among the most frequently used in practical statistics. Important references on this subject include Wilks ( 1962 ), Rao ( 1965 , pp. 347-352), and Agresti ( 1990 , pp. 434-435). We give proofs of some well-known results on the limiting distribution of D = −2log(λ), where λ is the likelihood ratio, under certain clearly-stated assumptions. We illustrate the theory by means of an example on contingency tables. Although results of this type are frequently used, the underlying theory is not always fully explained.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920600974229