article

Robust mixture regression using the t-distribution

Authors:

Chun YuAuthors Info & Claims

Computational Statistics & Data Analysis, Volume 71

Pages 116 - 127

Published: 01 March 2014 Publication History

Abstract

The traditional estimation of mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers or heavy-tailed errors. A robust mixture regression model based on the t-distribution by extending the mixture of t-distributions to the regression setting is proposed. However, this proposed new mixture regression model is still not robust to high leverage outliers. In order to overcome this, a modified version of the proposed method, which fits the mixture regression based on the t-distribution to the data after adaptively trimming high leverage points, is also proposed. Furthermore, it is proposed to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degrees of freedom.

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Cited By

Chang SLu KYang M(2019)Stepwise possibilistic c-regressionsInformation Sciences: an International Journal10.1016/j.ins.2015.11.042334:C(307-322)Online publication date: 6-Jan-2019
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Wu QYao W(2019)Mixtures of quantile regressionsComputational Statistics & Data Analysis10.1016/j.csda.2014.04.01493:C(162-176)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.csda.2014.04.014
Perthame EForbes FDeleforge A(2018)Inverse regression approach to robust nonlinear high-to-low dimensional mappingJournal of Multivariate Analysis10.1016/j.jmva.2017.09.009163:C(1-14)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1016/j.jmva.2017.09.009
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cover image Computational Statistics & Data Analysis

Computational Statistics & Data Analysis Volume 71, Issue

March, 2014

58 pages

ISSN:0167-9473

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2013.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 March 2014

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Cited By

Chang SLu KYang M(2019)Stepwise possibilistic c-regressionsInformation Sciences: an International Journal10.1016/j.ins.2015.11.042334:C(307-322)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.ins.2015.11.042
Wu QYao W(2019)Mixtures of quantile regressionsComputational Statistics & Data Analysis10.1016/j.csda.2014.04.01493:C(162-176)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.csda.2014.04.014
Perthame EForbes FDeleforge A(2018)Inverse regression approach to robust nonlinear high-to-low dimensional mappingJournal of Multivariate Analysis10.1016/j.jmva.2017.09.009163:C(1-14)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1016/j.jmva.2017.09.009
Zhao YWang PLi YLi M(2018)Fuzzy weighted c-harmonic regressions clustering algorithmSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-017-2642-322:14(4595-4611)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s00500-017-2642-3
Li MXiang SYao W(2018)Robust estimation of the number of components for mixtures of linear regression modelsComputational Statistics10.1007/s00180-015-0610-x31:4(1539-1555)Online publication date: 21-Dec-2018
https://dl.acm.org/doi/10.1007/s00180-015-0610-x
Punzo AIngrassia S(2018)Clustering bivariate mixed-type data via the cluster-weighted modelComputational Statistics10.1007/s00180-015-0600-z31:3(989-1013)Online publication date: 21-Dec-2018
https://dl.acm.org/doi/10.1007/s00180-015-0600-z
Hu HYao WWu Y(2017)The robust EM-type algorithms for log-concave mixtures of regression modelsComputational Statistics & Data Analysis10.1016/j.csda.2017.01.004111:C(14-26)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1016/j.csda.2017.01.004
García-Escudero LGordaliza AGreselin FIngrassia SMayo-Iscar A(2017)Robust estimation of mixtures of regressions with random covariates, via trimming and constraintsStatistics and Computing10.1007/s11222-016-9628-327:2(377-402)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s11222-016-9628-3
Punzo AMcnicholas P(2017)Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted ModelJournal of Classification10.1007/s00357-017-9234-x34:2(249-293)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s00357-017-9234-x
Nguyen HMcLachlan G(2016)Laplace mixture of linear expertsComputational Statistics & Data Analysis10.1016/j.csda.2014.10.01693:C(177-191)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.csda.2014.10.016
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