A new method for robust mixture regression. Issue 1 (29th December 2016)

• Record Type: Journal Article
• Authors: Yu, Chun; Yao, Weixin; Chen, Kun
• Is Part Of: Canadian journal of statistics. Volume 45:Issue 1(2017)
• Page Start: 77
• Page End: 94
• Publication Date: 2016-12-29
• Subjects: EM algorithm -- mixture regression models -- outlier detection -- penalized likelihood -- MSC 2010: Primary 62F35 -- secondary 62J99; Mathematical statistics -- Periodicals; 519.5
• DOI: 10.1002/cjs.11310
• Languages: English
• ISSNs: 0319-5724

Abstract

Abstract: Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity and wide applicability, may fail in the presence of severe outliers. Using a sparse, case‐specific, and scale‐dependent mean‐shift mixture model parameterization, we propose a robust mixture regression approach for simultaneously conducting outlier detection and robust parameter estimation. A penalized likelihood approach is adopted to induce sparsity among the mean‐shift parameters so that the outliers are distinguished from the remainder of the data, and a generalized Expectation–Maximization (EM) algorithm is developed to perform stable and efficient computation. The proposed approach is shown to have strong connections with other robust methods including the trimmed likelihood method and M‐estimation approaches. In contrast to several existing methods, the proposed methods show outstanding performance in our simulation studies. The Canadian Journal of Statistics 45: 77–94; 2017 © 2016 Statistical Society of Canada