Abstract
AbstractThe $$\gamma $$
γ
-divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the $$\gamma $$
γ
-divergence have been proposed. There are two types of $$\gamma $$
γ
-divergence for the regression problem, in which the base measures are handled differently. In this study, these two $$\gamma $$
γ
-divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One $$\gamma $$
γ
-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 $$\gamma $$
γ
is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
1 articles.
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1. Robust and sparse logistic regression;Advances in Data Analysis and Classification;2023-11-27