ABSTRACT

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.

摘要

在审查数据探索中，假设正态分布随机误差的经典线性回归模型可能是常用的框架之一。然而，实际研究经常批评经典线性回归模型，因为它对偏离正态性和部分非线性的敏感性。本文建议在部分线性回归模型的背景下同时解决这些潜在问题，方法是假设随机误差遵循正态 (SMN) 分布族的尺度混合。假设的方法使我们能够以极大的灵活性对数据进行建模，以适应重尾和异常值。通过实现 B 样条近似并使用 SMN 分布的方便分层表示，为了获得最大似然 (ML) 参数估计，开发了一种计算分析的 EM 类型算法。进行了各种模拟研究来研究有限样本的性质，以及模型在处理重尾分布数据集时的鲁棒性。最后分析了真实世界的数据示例，以说明所提出方法的有用性。