On the Asymptotic Distribution of the Likelihood Ratio Statistic

• Published in: Communications in statistics. Theory and methods Vol. 36; no. 2; pp. 273 - 281
• Main Author: Scott, W. F.
• Format: Journal Article
• Language: English
• 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
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920600974229

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.