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Title: Robust class of non-normal cluster-wise regression models Authors:  Elham Mirfarah - National Cheng Kung University (Taiwan) [presenting]
Mehrdad Naderi - National Chung Hsing University (Taiwan)
Wan-Lun Wang - National Cheng Kung University (Taiwan)
Tsung-I Lin - National Chung Hsing University (Taiwan)
Abstract: One of the widely used statistical frameworks for modelling, classification, and clustering of data is to adopt a mixture regression model (MRM), in which it is assumed that data coming from several hidden clusters have different regression functions. Since the conventional MRMs are sensitive to departures from normality, caused by extra skewness and possible heavy tails, various extensions built on flexible distributions have been put forward in the last decade. The class of normal mean-variance mixture (NMVM) distributions that arise from scaling both the mean and variance of a normal random variable with a common mixing distribution encompasses many prominent (symmetric or asymmetrical) distributions as special cases. We aim to introduce a unified approach to robustifying MRMs by considering the class of NMVM distributions for component errors. An analytical expectation-maximization (EM) type algorithm is developed to obtain the maximum likelihood parameter estimates. The finite-sample performance, effectiveness, and robustness of the proposed model against outliers for contaminated and noisy data are illustrated by conducting four simulation studies and analyzing two real-world datasets.