## The Annals of Statistics

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

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

David S. Moore and M. C. Spruill

#### 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