Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 3, pp. 315--337

DIVERGENCE MEASURES BASED ON ENTROPY FUNCTIONS AND STATISTICAL INFERENCE

By

L. PARDO,  Universidad Complutense de Madrid

M. SALICRÚ,  Universidad de Barcelona

M. L. MENÉNDEZ,  Universidad Politécnica de Madrid

and

D. MORALES,  Universidad Complutense de Madrid

SUMMARY. Using divergence measures based on entropy functions, a procedure to test statistical hypotheses is proposed. Replacing the parameters by suitable estimators in the expression of the divergence measure, the test statistics are obtained. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are used. These results can also be applied to multinomial populations. Tests of goodness of fit and tests of homogeneity can be constructed.

AMS (1991) subject classification.  Primary 62B10; secondary 62E20.

Key words and phrases. $R^{h}_{/phi}$- Divergence statistics, maximum likelihood estimators, asymptotic distributions, testing statistical hypotheses.

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