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In the framework of censored data modeling, the classical linear regression model that assumes normally distributed random errors has received increasing attention in recent years, mainly for mathematical and computational convenience. However, practical studies have often criticized this linear regression model due to its sensitivity to departure from the normality and from the partial nonlinearity. This paper proposes to solve these potential issues simultaneously in the context of the partial linear regression model by assuming that the random errors follow a scale-mixture of normal (SMN) family of distributions. The proposed method allows us to model data with great flexibility, accommodating heavy tails, and outliers. By implementing the B-spline function and using the convenient hierarchical representation of the SMN distributions, a computationally analytical EM-type algorithm is developed to perform maximum likelihood inference of the model parameters. Various simulation studies are conducted to investigate the finite sample properties as well as the robustness of the model in dealing with the heavy-tails distributed datasets. Real-word data examples are finally analyzed for illustrating the usefulness of the proposed methodology., Comment: 17 page, 4 figures

The classical mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and computational convenience, the classical MoE model has two challenges: 1) it is sensitive to atypical observations and outliers, and 2) it might produce misleading inferential results for censored data. The paper is then aimed to resolve these two challenges, simultaneously, by proposing a novel robust MoE model for model-based clustering and discriminant censored data with the scale-mixture of normal class of distributions for the unobserved error terms. Based on this novel model, we develop an analytical expectation-maximization (EM) type algorithm to obtain the maximum likelihood parameter estimates. Simulation studies are carried out to examine the performance, effectiveness, and robustness of the proposed methodology. Finally, real data is used to illustrate the superiority of the new model., Comment: 21 pages