Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 3, pp. 365--376

COMPARISONS OF THE BLENDED WEIGHT HELLINGER DISTANCE BASED GOODNESS-OF-FIT TEST STATISTICS

By

DONG WAN SHIN, University of Suwon

AYANENDRANATH BASU,  University of Texas at Austin

and

SAHADEB SARKAR,  Oklahama State University

SUMMARY. The class of goodness-of-fit tests based on the blended weight Hellinger distance (BWHD) is a rich subfamily of the family of disparity tests introduced by Basu & Sarkar (1994a). In small samples, for most members of the BWHD family, the limiting chi-square null distribution can produce significance levels that are very different from the desired nominal levels. In this paper we derive three alternative approximations of their exact distributions, leading to more accurate significance levels. Numerical results are presented for the symmetric null hypothesis for different multinomial sample sizes with various cell numbers. Exact power comparisons under specific alternatives to the symmetric null hypothesis show that the well known Pearson's chi-square have smaller power than some other members of the BWHD family.

AMS (1991) subject classification.  Primary 62F03, 62F04, 62F05; Secondary 62H15.

Key words and phrases. Goodness-of-fit, chi-squared statistic, blended weight Hellinger distance, hellinger distance, large sparse multinomial, likelihood ratio test.

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This article in mathematical reviews.