The Annals of Statistics

Efficiencies of Chi-Square and Likelihood Ratio Goodness-of-Fit Tests

M. P. Quine and J. Robinson

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The classical problem of choice of number of classes in testing goodness of fit is considered for a class of alternatives, for the chi-square and likelihood ratio statistics. Pitman and Bahadur efficiencies are used to compare the two statistics and also to analyse the effect for each statistic of changing the number of classes for the case where the number of classes increases asymptotically with the number of observations. Overall, the results suggest that if the class of alternatives is suitably restricted the number of classes should not be very large.

Article information

Ann. Statist., Volume 13, Number 2 (1985), 727-742.

First available in Project Euclid: 12 April 2007

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Primary: 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

Pitman efficiency Bahadur efficiency chi-square likelihood ratio goodness-of-fit central limit theorem large deviations


Quine, M. P.; Robinson, J. Efficiencies of Chi-Square and Likelihood Ratio Goodness-of-Fit Tests. Ann. Statist. 13 (1985), no. 2, 727--742. doi:10.1214/aos/1176349550.

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