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Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter [Formula: see text] , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers...

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Detalles Bibliográficos
Autores principales: Riani, Marco, Atkinson, Anthony C., Corbellini, Aldo, Perrotta, Domenico
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516876/
https://www.ncbi.nlm.nih.gov/pubmed/33286173
http://dx.doi.org/10.3390/e22040399
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author Riani, Marco
Atkinson, Anthony C.
Corbellini, Aldo
Perrotta, Domenico
author_facet Riani, Marco
Atkinson, Anthony C.
Corbellini, Aldo
Perrotta, Domenico
author_sort Riani, Marco
collection PubMed
description Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter [Formula: see text] , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power [Formula: see text]. We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of [Formula: see text] leading to more efficient parameter estimates.
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spelling pubmed-75168762020-11-09 Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis Riani, Marco Atkinson, Anthony C. Corbellini, Aldo Perrotta, Domenico Entropy (Basel) Article Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter [Formula: see text] , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power [Formula: see text]. We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of [Formula: see text] leading to more efficient parameter estimates. MDPI 2020-03-31 /pmc/articles/PMC7516876/ /pubmed/33286173 http://dx.doi.org/10.3390/e22040399 Text en © 2020 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Riani, Marco
Atkinson, Anthony C.
Corbellini, Aldo
Perrotta, Domenico
Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title_full Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title_fullStr Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title_full_unstemmed Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title_short Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis
title_sort robust regression with density power divergence: theory, comparisons, and data analysis
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516876/
https://www.ncbi.nlm.nih.gov/pubmed/33286173
http://dx.doi.org/10.3390/e22040399
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