  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.
