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Title: Robust mixture modeling by mean shift parameters Authors:  Weixin Yao - UC Riverside (United States) [presenting]
Chun Yu - Jiangxi University of Finance and Economics (China)
Kun Chen - University of Connecticut (United States)
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 of its simplicity and wide applicability, may fail in the presence of severe outliers. We propose a new robust mixture regression approach based on a sparse, case-specific, and scale-dependent mean-shift mixture model parameterization, 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 good observations, and a thresholding-embedded Expectation-Maximization (EM) algorithm is developed to enable stable and efficient computation. The proposed penalized estimation approach is shown to have strong connections with other robust methods including the trimmed likelihood method and the M-estimation approaches. Comparing with several existing methods, the proposed methods show outstanding performance in our numerical studies.