Uniform in bandwidth consistency of the kernel-type estimator of the Shannon’s entropy

Published in Comptes Rendus Academie des Sciences, Series I, Mathematics, 2010

S. Bouzebda and I. Elhattab

We establish uniform-in-bandwidth consistency for kernel-type estimators of the differential entropy. We consider two kernel-type estimators of Shannon’s entropy. As a consequence, an asymptotic \(100\%\) confidence interval of entropy is provided.

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