The Annals of Statistics

Generalized Chi-Square Goodness-of-Fit Tests for Location-Scale Models when the Number of Classes Tends to Infinity

F. C. Drost

Full-text: Open access

Abstract

In this paper we consider generalized chi-square goodness-of-fit tests based on increasingly finer partitions (as the sample size increases) for models with location-scale nuisance parameters. The asymptotic distributions are derived both under the null hypothesis and under local alternatives, obtained by taking contamination families of densities between the null hypothesis and fixed alternative hypotheses. If the number of random cells increases to infinity, the Rao-Robson-Nikulin test statistic is shown to be superior to the Watson-Roy and Dzhaparidze-Nikulin statistics. Conditions are derived under which it is optimal to let the number of classes tend to infinity.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1285-1300.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347269

Digital Object Identifier
doi:10.1214/aos/1176347269

Mathematical Reviews number (MathSciNet)
MR1015151

Zentralblatt MATH identifier
0683.62011

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62F05: Asymptotic properties of tests 62F10: Point estimation 62F20

Keywords
Generalized chi-square tests Rao-Robson-Nikulin statistic Watson-Roy statistic Dzhaparidze-Nikulin statistic location-scale model nuisance parameters number of classes goodness-of-fit

Citation

Drost, F. C. Generalized Chi-Square Goodness-of-Fit Tests for Location-Scale Models when the Number of Classes Tends to Infinity. Ann. Statist. 17 (1989), no. 3, 1285--1300. doi:10.1214/aos/1176347269. https://projecteuclid.org/euclid.aos/1176347269


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