Robust regression against heavy heterogeneous contamination View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2022-07-01

AUTHORS

Takayuki Kawashima, Hironori Fujisawa

ABSTRACT

The γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-divergence have been proposed. There are two types of γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-divergence for the regression problem, in which the base measures are handled differently. In this study, these two γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-divergence has the strong robustness even under heterogeneous contamination. The other does not have in general; however, it has under homogeneous contamination, where the outlier ratio does not depend on the explanatory variable, or when the parametric model of the response variable belongs to a location-scale family in which the scale does not depend on the explanatory variables. Hung et al. (Biometrics 74(1):145–154, 2018) discussed the strong robustness in a logistic regression model with an additional assumption that the tuning parameter γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption. More... »

PAGES

1-22

References to SciGraph publications

  • 2020-09-30. Robust high-dimensional regression for data with anomalous responses in ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
  • 1988-12-01. Monotonicity of quadratic-approximation algorithms in ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
  • 1989. Generalized Linear Models in NONE
  • 2015-05-28. Robust estimation in generalized linear models: the density power divergence approach in TEST
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    http://scigraph.springernature.com/pub.10.1007/s00184-022-00874-1

    DOI

    http://dx.doi.org/10.1007/s00184-022-00874-1

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    https://app.dimensions.ai/details/publication/pub.1149154541


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