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Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators

We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities....

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Detalles Bibliográficos
Autores principales: Ding, Rui, Mullhaupt, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137612/
https://www.ncbi.nlm.nih.gov/pubmed/37190400
http://dx.doi.org/10.3390/e25040612
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author Ding, Rui
Mullhaupt, Andrew
author_facet Ding, Rui
Mullhaupt, Andrew
author_sort Ding, Rui
collection PubMed
description We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities. We illustrate the proposed estimator on several one-dimensional probability distributions. Finally, we extend the estimator to a family of estimators for the family of [Formula: see text]-divergences, which almost surely converge as well, and discuss the uniqueness of this result. We demonstrate applications of the proposed Hellinger affinity estimators to approximately bounding the Neyman–Pearson regions.
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spelling pubmed-101376122023-04-28 Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators Ding, Rui Mullhaupt, Andrew Entropy (Basel) Article We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities. We illustrate the proposed estimator on several one-dimensional probability distributions. Finally, we extend the estimator to a family of estimators for the family of [Formula: see text]-divergences, which almost surely converge as well, and discuss the uniqueness of this result. We demonstrate applications of the proposed Hellinger affinity estimators to approximately bounding the Neyman–Pearson regions. MDPI 2023-04-04 /pmc/articles/PMC10137612/ /pubmed/37190400 http://dx.doi.org/10.3390/e25040612 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Ding, Rui
Mullhaupt, Andrew
Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title_full Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title_fullStr Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title_full_unstemmed Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title_short Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
title_sort empirical squared hellinger distance estimator and generalizations to a family of α-divergence estimators
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137612/
https://www.ncbi.nlm.nih.gov/pubmed/37190400
http://dx.doi.org/10.3390/e25040612
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