Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 2, 179--191

SCORE TEST FOR GOODNESS OF FIT OF GENERALIZED LINEAR MODELS

TO SPARSE DATA

By

SUDHIR R. PAUL

and

DIANLIANG DENG, University of Windsor, Canada

SUMMARY. We develop a score test statistic based on quasi-score functions for goodness of fit of generalized linear models to sparse data. A modified score test statistic is also obtained. The modified score test statistic has a simple form and is closely related to the test statistic based on the modified Pearson statistic developed by Farrington (1996). The modified score test statistic is greater than or equal to the standardized modified Pearson statistic. For Poisson data the modified score test statistic is identical to the standardized modified Pearson statistic. For binomial data the modified score test statistic is, in general, more powerful than the test based on the modified Pearson statistic. The gain in power of the modified Pearson statistic and the modified score statistic over the score statistic may be substantial.

AMS (1991) subject classification}. Primary 62J12, 62J05; secondary 62F05..

Key words and phrases. Binomial data, modified score test, Poisson data, power, size, sparse data, standardized modified Pearson statistic.

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