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In recent years, a number of results have been developed which connectinformation measures and estimation measures under various models, including,predominently, Gaussian and Poisson models. More recent results due to Tabordaand Perez-Cruz relate the relative entropy to certain mismatched estimationerrors in the context of binomial and negative binomial models, where, unlikein the case of Gaussian and Poisson models, the conditional mean estimatesconcern models of different parameters than those of the original model. Inthis note, a different set of results in simple forms are developed forbinomial and negative binomial models, where the conditional mean estimates areproduced through the original models. The new results are more consistent withexisting results for Gaussian and Poisson models.

Information and Estimation over Binomial and Negative Binomial Models