In many studies, limited or censored data are collected. This occurs, in many situations in practice, 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 covariate in the linear predictor. In this work, 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. The package PartCensReg implemented for the software R give computational support to this work.

中文翻译：

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基于重尾分布的部分线性删失回归模型的估计和诊断

在许多研究中，收集的数据有限或经过审查。在实践中的许多情况下，由于测量仪器的限制或由于实验设计等原因，会发生这种情况。因此，响应可以是左删失、间隔删失或右删失。另一方面，部分线性模型被认为是线性回归模型的灵活概括，通过在线性预测变量中包含一些协变量的非参数分量。在这项工作中，我们讨论了部分线性删失回归模型中的估计和诊断程序，其中误差遵循正态 (SMN) 分布的尺度混合。该分布族包含一组众所周知的重尾分布，通常用于对对称数据进行稳健推断，例如 Student-t、斜线和污染正态分布等。提出了一种用于迭代计算参数的最大惩罚似然 (MPL) 估计的简单 EM 型算法。为了检查所提出模型的性能，开发了案例删除和局部影响技术，以显示其对外围和有影响的观察结果的鲁棒性。这是通过在模型或数据中的一些常用扰动方案下对最大惩罚似然估计进行敏感性分析，并通过检查一些建议的诊断图来执行的。我们通过经验实验评估算法的有限样本性能和 MPL 估计的渐近特性。提出了对真实数据集的应用，以说明所提出方法的有效性。