The Annals of Statistics

Unified Large-Sample Theory of General Chi-Squared Statistics for Tests of Fit

David S. Moore and M. C. Spruill

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Abstract

We present a unified large-sample theory of general chi-squared tests of fit under composite null hypotheses and Pitman alternatives. The statistics are quadratic forms in the standardized cell frequencies, and we allow random cells, $k$-variate observations from not necessarily continuous distributions, and quite general estimates of unknown parameters. Generalizations of published results on a number of specific chi-squared tests follow.

Article information

Source
Ann. Statist., Volume 3, Number 3 (1975), 599-616.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343125

Digital Object Identifier
doi:10.1214/aos/1176343125

Mathematical Reviews number (MathSciNet)
MR375569

Zentralblatt MATH identifier
0322.62047

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G10: Hypothesis testing

Keywords
Chi-squared tests goodness of fit limiting distributions

Citation

Moore, David S.; Spruill, M. C. Unified Large-Sample Theory of General Chi-Squared Statistics for Tests of Fit. Ann. Statist. 3 (1975), no. 3, 599--616. doi:10.1214/aos/1176343125. https://projecteuclid.org/euclid.aos/1176343125


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