The Annals of Statistics

Unbiasedness of the Chi-Square, Likelihood Ratio, and Other Goodness of Fit Tests for the Equal Cell Case

Arthur Cohen and H. B. Sackrowitz

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Abstract

The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.

Article information

Source
Ann. Statist. Volume 3, Number 4 (1975), 959-964.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343197

Digital Object Identifier
doi:10.1214/aos/1176343197

Mathematical Reviews number (MathSciNet)
MR381087

Zentralblatt MATH identifier
0311.62021

JSTOR
links.jstor.org

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 62G10: Hypothesis testing

Keywords
Hypothesis testing chi-square test likelihood ratio tests goodness of fit tests unbiasedness Type D.

Citation

Cohen, Arthur; Sackrowitz, H. B. Unbiasedness of the Chi-Square, Likelihood Ratio, and Other Goodness of Fit Tests for the Equal Cell Case. Ann. Statist. 3 (1975), no. 4, 959--964. doi:10.1214/aos/1176343197. https://projecteuclid.org/euclid.aos/1176343197


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