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Uniform-in-bandwidth consistency for kernel-type estimators of Shannon’s entropy

Salim Bouzebda, Issam Elhattab

Electronic Journal of Statistics · 2011 · 37 citations · 33 references

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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.

References

33

A Mathematical Theory of Communication

Claude E. Shannon · Bell System Technical Journal · 1948 · 80.7K citations

, , +11

Information Theory and Statistical Mechanics

E. T. Jaynes · Physical Review · 1957 · 12.9K citations

, , +9

On Estimation of a Probability Density Function and Mode

Emanuel Parzen · The Annals of Mathematical Statistics · 1962 · 10.5K citations · Full text

, , +9

Information theory and statistics

Journal of the Franklin Institute · 1959 · 7.2K citations

, , +12

Remarks on Some Nonparametric Estimates of a Density Function

Murray Rosenblatt · The Annals of Mathematical Statistics · 1956 · 4.5K citations · Full text

, , +12