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In the censored data exploration, the classical linear regression model which assumes normally distributed random errors is perhaps one of the commonly used frameworks. However, practical studies have often criticized the classical linear regression model because of its sensitivity to departure from the normality and 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 postulated method allows us to model data with great flexibility, accommodating heavy tails and outliers. By implementing the B-spline approximation and using the convenient hierarchical representation of the SMN distributions, a computationally analytical EM-type algorithm is developed for obtaining maximum likelihood (ML) parameter estimates. 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-world data examples are finally analyzed for illustrating the usefulness of the proposed methodology.

Semiparametric inference for the scale-mixture of normal partial linear regression model with censored data