Statistics and Its Interface

Volume 14 (2021)

Number 2

Estimation and diagnostics for partially linear censored regression models based on heavy-tailed distributions

Pages: 165 – 182

DOI: https://dx.doi.org/10.4310/20-SII624

Authors

Marcela Nuñez Lemus (Departamento de Estatística, Universidade Estadual de Campinas, Cidade Universitária, SP, Brazil)

Victor H. Lachos (Department of Statistics, University of Connecticut, Storrs, Ct., U.S.A.)

Christian E. Galarza (Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, Guayaquil, Ecuador)

Larissa A. Matos (Departamento de Estatística, Universidade Estadual de Campinas, Cidade Universitária, SP, Brazil)

Abstract

In many studies, limited or censored data are collected. This occurs, in several practical situations, for reasons such as limitations of measuring instruments or due to experimental design. So, the responses can be either left, interval or right censored. On the other hand, partially linear models are considered as a flexible generalizations of linear regression models by including a nonparametric component of some covariates in the linear predictor. In this paper, we discuss estimation and diagnostic procedures in partially linear censored regression models with errors following a scale mixture of normal (SMN) distributions. This family of distributions contains a group of well-known heavy-tailed distributions that are often used for robust inference of symmetrical data, such as Student‑t, slash and contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum penalized likelihood (MPL) estimates of the parameters is presented. To examine the performance of the proposed model, case-deletion and local influence techniques are developed to show its robustness against outlying and influential observations. This is performed by sensitivity analysis of the maximum penalized likelihood estimates under some usual perturbation schemes, either in the model or in the data, and by inspecting some proposed diagnostic graphs. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the MPL estimates through empirical experiments. An application to a real dataset is presented to illustrate the effectiveness of the proposed methods. Both estimation procedure and diagnostic tools were implemented in the $\texttt{RPartCensReg}$ package.

Keywords

censored regression model, EM-type algorithm, partially linear models, local influence, scale mixtures of normal distributions

Received 7 September 2019

Accepted 15 June 2020

Published 22 December 2020