Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 69--80

SOME PROPERTIES OF THE KULLBACK-LEIBLER NUMBER

By

NARASIMHA R. CHAGANTY, Old Dominion University

and

RAJEEVA L. KARANDIKAR, Indian Statistical Institute

SUMMARY.  In this paper we obtain some useful properties of the Kullback-Liebler (K-L) number. For example, we show that the K-L number is jointly lower semi-continuous in both arguments, on the class of probability measures endowed with weak topology. We use some of these properties to obtain a generalization of Senov's theorem, and establish the large deviation principle for the bootstrap empirical measure, for almost all infinite sample sequences.

AMS (1991) subject classification.  Primary 60F10, 62G09, 62G30.

Key words and phrases. Bootstrap, large deviations empirical measure, Kullback-Leibler number.

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