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

Bouzebda, Salim; Elhattab, Issam

doi:10.1214/11-ejs614

Cited by 34 publications

(21 citation statements)

References 34 publications

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“…In other words, the fluctuation of the bandwidth in a small interval do not affect the consistency of the nonparametric estimators of these divergences. The work of Bouzebda and Elhattab [2] is very important for establishing our results, these authors have created a class of compactly supported densities. They used the following additional conditions.…”

Section: Statistical Properties Of the Estimatorsmentioning

confidence: 85%

“…The approach used to define the plug-in estimators is also developed in [2] in order to introduce a kernel-type estimator of Shannon's entropy. Some statistical properties of these divergences is related to those of the kernel estimator 9,G H ⋅ of the continuous density .…”

Section: Kernel-type Estimators Of Divergence Measuresmentioning

confidence: 99%

“…Unlike of their frameworks, we study the strong consistency estimators for a general class of divergence measures. We emphasize that the plug-in estimation techniques are heavily used by [2,9] in the case of entropy. Bouzebda [2] proposed a method to establish consistency for kernel-type estimators of the differential entropy.…”

Section: Introductionmentioning

confidence: 99%

“…We emphasize that the plug-in estimation techniques are heavily used by [2,9] in the case of entropy. Bouzebda [2] proposed a method to establish consistency for kernel-type estimators of the differential entropy. We generalize this method for a large class of divergence measures in order to establish the consistency of kernel-type estimators of divergence measure when the bandwidth is allowed to range in a small interval which may decrease in length with the sample size.…”

Section: Introductionmentioning

confidence: 99%

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Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency

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Nonparametric density estimation, based on kernel-type estimators, is a very popular method in statistical research, especially when we want to model the probabilistic or stochastic structure of a data set. In this paper, we investigate the asymptotic confidence bands for the distribution with kernel-estimators for some types of divergence measures (Rényi-α and Tsallis-α divergence). Our aim is to use the method based on empirical process techniques, in order to derive some asymptotic results. Under different assumptions, we establish a variety of fundamental and theoretical properties, such as the strong consistency of an uniform-in-bandwidth of the divergence estimators. We further apply the previous results in simulated examples, including the kernel-type estimator for Hellinger, Bhattacharyya and Kullback-Leibler divergence, to illustrate this approach, and we show that that the method performs competitively.

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Section: Statistical Properties Of the Estimatorsmentioning

confidence: 85%

Section: Kernel-type Estimators Of Divergence Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency

Dhaker

Ngom

Dème³

et al. 2016

AJTAS

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“…respectively developed in [2] and [15] in order to introduce a kernel-type estimators of Shannon's entropy and divergences.…”

Section: Nonparametric Estimation Ofmentioning

confidence: 99%

Generalized Divergence Criteria for Model Selection Between Random Walk and Ar(1) Model

Dhaker

Ngom

Mendy

et al. 2017

Jour. Stat. Adv. Theory and Appl.

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We introduce a kernel-type estimators of ( ) φ /, v -divergence for continuous distributions. We discuss this approach of goodness-of-fit test for a model selection criterion relative to these divergence measures. Our interest is in the problem to testing for choosing between two models using some informational type statistics (on random walk and autoregressive AR (1)). The limit laws of the estimates and test statistics are given under both the null and the alternative hypotheses. We also describe how to apply estimators and illustrate their efficiency through numerical experiences. DHAKER HAMZA et al. 84

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Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method

Bouzebda

Slaoui²

2022

Sankhya A

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

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.

Cited by 34 publications

References 34 publications

Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency

Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency

Generalized Divergence Criteria for Model Selection Between Random Walk and Ar(1) Model

Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method

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