The Annals of Statistics

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

M. P. Quine and J. Robinson

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349550

Digital Object Identifier
doi:10.1214/aos/1176349550

Mathematical Reviews number (MathSciNet)
MR790568

Zentralblatt MATH identifier
0576.62061

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176349550


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