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Improved Likelihood Ratio Tests for Complete Contingency Tables

David A. Williams

Open publisher page 18 citations

Abstract

Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the −2logλtest statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic X2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators.

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What this paper is about

Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the −2logλtest statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic X2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators.

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Available abstract

Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the −2logλtest statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic X2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators.

Key concepts: Mathematics, Contingency table, Likelihood-ratio test, Score test, Statistics, Statistic, Null distribution, Asymptotic distribution

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