Abstract

A maximum likelihood estimator of a linear regression model is efficient relative to the customary Ordinary Least Squares (OLS) estimator when disturbances are skewed and/or thick-tailed. In order to model skewed and thick-tailed disturbances, we specify a highly flexible Generalized Tukey Lambda (GTL) distribution that can closely mimic many other unimodal distributions. The GTL-based maximum likelihood regression estimator is consistent and asymptotically normal. A Monte Carlo study demonstrates the potential gains of this GTL-based estimator over the OLS estimator, and as a real-life application, an analysis of speeding tickets illustrates how GTL regression might modify standard OLS estimation results. For the applied data analyst, an LM test statistic is suggested as a straightforward post-estimation diagnostic of whether the standard OLS regression approach is suitable for the data at hand. Stata do-files are provided to perform the OLS post-estimation LM test and to implement GTL regression models.

摘要

当扰动偏斜和/或厚尾时，线性回归模型的最大似然估计量相对于惯用的普通最小二乘 (OLS) 估计量更为有效。为了对偏斜和厚尾扰动进行建模，我们指定了一种高度灵活的广义 Tukey Lambda (GTL) 分布，它可以密切模仿许多其他单峰分布。基于 GTL 的最大似然回归估计器是一致的且渐近正态的。蒙特卡罗研究证明了这种基于 GTL 的估计器相对于 OLS 估计器的潜在增益，并且作为现实生活中的应用，对超速罚单的分析说明了 GTL 回归如何修改标准 OLS 估计结果。对于应用数据分析师来说，建议使用 LM 检验统计量作为标准 OLS 回归方法是否适合手头数据的简单后估计诊断。提供 Stata do 文件来执行 OLS 后估计 LM 测试并实现 GTL 回归模型。