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Uniform-in-bandwidth consistency for kernel-type estimators of shannon's entropy

Electronic Journal of Statistics (2011) 5 440-459
DOI: 10.1214/11-EJS614
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Abstract

We establish uniform-in-bandwidth consistency for kernel-type estimators of the differential entropy. We consider two kernel-type estima-tors of Shannon's entropy. As a consequence, an asymptotic 100% confi-dence interval of entropy is provided.

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Bouzebda, S., & Elhattab, I. (2011). Uniform-in-bandwidth consistency for kernel-type estimators of shannon’s entropy. Electronic Journal of Statistics, 5, 440–459. https://doi.org/10.1214/11-EJS614

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