## The Annals of Statistics

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

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

#### 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