## The Annals of Statistics

### A Comparison of Chi-Square Goodness-of-Fit Tests Based on Approximate Bahadur Slope

M. C. Spruill

#### Abstract

The Pearson-Fisher $\chi^2$ statistic is asymptotically chi-square under the null hypothesis with $M - m - 1$ degrees of freedom where $M =$ number of cells and $m =$ dimension of parameter. The Chernoff-Lehmann statistic is a weighted sum of chi-squares and the Kambhampati statistic is $\chi^2$ with $M - 1$ degrees of freedom. The approximate Bahadur slopes of the tests based on these statistics are computed. It is shown that the Kambhampati test always dominates the Chernoff-Lehmann and that no such dominance exists between the Pearson-Fisher test and Kambhampati test, or the Pearson-Fisher and Chernoff-Lehmann.

#### Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 409-412.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343418

Digital Object Identifier
doi:10.1214/aos/1176343418

Mathematical Reviews number (MathSciNet)
MR391380

Zentralblatt MATH identifier
0326.62036

JSTOR