Uniform-in-bandwidth consistency for kernel-type estimators of Shannon's entropy
Salim Bouzebda (LSTA), Issam Elhattab (LSTA)
TL;DR
This paper proves uniform-in-bandwidth consistency for kernel estimators of Shannon's entropy and provides an asymptotic confidence interval, advancing the theoretical understanding of entropy estimation.
Contribution
It introduces and proves uniform-in-bandwidth consistency for two kernel-type estimators of Shannon's entropy, including an asymptotic confidence interval.
Findings
Established uniform-in-bandwidth consistency for kernel entropy estimators
Derived an asymptotic 100% confidence interval for entropy
Enhanced theoretical foundation for entropy estimation methods
Abstract
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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