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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....
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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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. |
format | Online Article Text |
id | pubmed-10137612 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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