Electronic Journal of Statistics

Multinomial goodness-of-fit tests under inlier modification

Abhijit Mandal and Ayanendranath Basu

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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

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

First available in Project Euclid: 22 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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