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.