Parameter estimation and the variable selection are two pioneer issues in regression analysis. While traditional variable selection methods require prior estimation of the model parameters, the penalized methods simultaneously carry on parameter estimation and variable select. Therefore, penalized variable selection methods are of great interest and have been extensively studied in literature. However, most of the papers in literature are only limited to the regression models with uncorrelated error terms and normality assumption. In this study, we combine the parameter estimation and the variable selection in regression models with autoregressive error term by using different penalty functions under heavy tailed error distribution assumption. We conduct a simulation study and a real data example to show the performance of the estimators.

翻译：参数估计和变量选择是回归分析的两个先驱问题。传统变量选择方法要求先对模型参数进行估计,但受处罚的方法同时进行参数估计和变量选择。因此,受处罚的变量选择方法引起了极大的兴趣,并已在文献中进行了广泛研究。然而,文献中的大多数论文仅局限于回归模型,有不相干错误条件和正常度假设。在本研究中,我们将参数估计和回归模型中的变量选择与自回归错误术语结合起来,在严重尾随错误分布假设下使用不同的处罚函数。我们进行模拟研究和真实数据示例,以显示估算员的性能。