ESTIMATION OF THE KULLBACK-LEIBLER DIVERGENCE
Résumé
The Kullback-Leibler (KL) divergence K(fl, P) between a set O of probability measures (PMs) on ]R d and some PM P cannot be estimated by K(O, Pn) when O contains PM whose support is not included in the support of the empirical measure Pn. We propose an estimation procedure which avoids any smoothing of Pn. Also we provide an estimate of the derivative of the projected measure with respect to P. We make use of the representation of the KL divergence in terms of the Fenchel-Le ge ndre transform of the moment generating function. As an application we introduce some new technique in parametric estimation, and also apply our results to updating problems.
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