Layman's abstract: A new method for robust mixture regression

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  • Author: Chun Yu, Weixin Yao, Kun Chen
  • Date: 10 November 2017
  • Copyright: © Statistical Society of Canada

Every Friday on Statistics Views, we publish layman's abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format. This article featured today is from The Canadian Journal of Statistics: A new method for robust mixture regression by Chun Yu, Weixin Yao, Kun Chen.

Read the layman's abstract below.

Chun Yu, Weixin Yao, Kun Chen. (2017), A new method for robust mixture regression, The Canadian Journal of Statistics, 45, pages 77-94, doi: 10.1002/cjs.11310

thumbnail image: Layman's abstract: A new method for robust mixture regression

Suppose that the population consists of several heterogeneous components and the response y and predictor x’s have homogeneous linear regression relationship in each component, then the population can be modeled by a finite mixture regression model. Finite mixture regression model has been widely used in business, marketing, social sciences, etc. The traditional method for parameter estimation is the maximum likelihood estimate (MLE).However, MLE fails in the presence of severer outliers. Therefore, robust techniques become necessary in order to resist the influence of outliers on mixture regression model.

A new approach, which is called robust mixture regression via mean-shift penalization (RM2) is proposed in this paper. The proposed approach can achieve simultaneous outlier detection and parameter estimation. A robust mixture regression model is built by adding a scale-free mean-shift parameter in the classical mixture regression model. The estimate of the mean-shift parameter can tell whether an observation is an outlier or not. An observation is regarded as an outlier if the corresponding mean-shift parameter is estimated nonzero. A penalized likelihood approach is adopted to induce sparsity among the mean-shift parameters, that is, most of the mean-shift parameters are estimated to be zero, so that the outliers are distinguished from the remainder of the data. A generalized Expectation-Maximization (EM) algorithm is developed to perform stable and efficient computation for parameter estimation. In contrast to several existing methods, the proposed method show outstanding performance in the simulation studies.

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