Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 1, pp.72--92

MINIMUM PHI-DIVERGENCE ESTIMATOR FOR HOMOGENEITY IN MULTINOMIAL POPULATIONS*

By

L. PARDO and M.C. PARDO, Complutense University of Madrid, Spain

and

K. ZOGRAFOS, University of Ioannina, Greece

SUMMARY. In this paper we present a new family of statistics for the problem of homogeneity when the estimation of some parameters is necessary. We consider the minimum $\varphi$-divergence estimator of the parameters instead of the maximum likelihood estimator and a family of statistics based on Phi-divergence as a generalization of the usual chi-square statistic.

AMS (1991) subject classification. 62H15, 62F12.

Key words and phrases. Asymptotic distributions, phi-divergence, Minimum phi-divergence estimator, testing statistical hypotheses, homogeneity.

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