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

TL;DR

This paper introduces a flexible semiparametric partial linear regression model for censored data, utilizing scale-mixture of normal errors to handle heavy tails and outliers, with an EM algorithm for inference.

Contribution

It proposes a novel semiparametric approach combining scale-mixture of normal errors with partial linear regression for censored data, enhancing robustness and flexibility.

Findings

The model effectively handles heavy-tailed and outlier data.

Simulation studies demonstrate good finite sample properties.

Real data analysis confirms practical usefulness.

Abstract

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.