Electronic Journal of Statistics

Multinomial goodness-of-fit tests under inlier modification

Abhijit Mandal and Ayanendranath Basu

Full-text: Open access

Abstract

The Pearson’s chi-square and the log-likelihood ratio chi-square statistics are fundamental tools in multinomial goodness-of-fit testing. Cressie and Read (1984) constructed a general family of divergences which includes both statistics as special cases. This family is indexed by a single real parameter. Divergences at one end of the scale are powerful against deviations of one type while being poor against deviations of the other type. The reverse property holds for divergences at the other end of the scale. Several other families of divergences available in the literature also show similar behavior. We present several inlier control techniques in the context of multinomial goodness-of-fit testing which generate procedures having reasonably high powers for both kinds of alternatives. We explain the motivation behind the construction of the inlier modified test statistics, establish the asymptotic null distribution of the inlier modified statistics and explore their performance through simulation and real data examples to substantiate the theory developed.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1846-1875.

Dates
First available in Project Euclid: 22 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1324563947

Digital Object Identifier
doi:10.1214/11-EJS658

Mathematical Reviews number (MathSciNet)
MR2870152

Zentralblatt MATH identifier
1271.62110

Subjects
Primary: 62G35: Robustness
Secondary: 62G10: Hypothesis testing

Keywords
Goodness-of-fit disparity inliers power divergence small sample studies

Citation

Mandal, Abhijit; Basu, Ayanendranath. Multinomial goodness-of-fit tests under inlier modification. Electron. J. Statist. 5 (2011), 1846--1875. doi:10.1214/11-EJS658. https://projecteuclid.org/euclid.ejs/1324563947


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