Abstract

A large amount of literature has been developed for the presence of multicollinearity among the explanatory variables that are often performed with the aim of reducing the undesirable effects on the maximum likelihood estimate(MLE). In particular, many authors have discussed ridge estimation (RE) under the framework of the mean regression model, because the RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. However, most of the existing methods assume or are applicable to symmetrical data. In this paper, we consider the case of skewed (or asymmetrical) data, which often occur in practice and include symmetrical data as a special case, and derive the RE of the skew-mormal mode regression model under multicollinearity problem. A maximum likelihood method via an EM algorithm and the eleven ridge parameter methods are investigated. Monte Carlo simulation results indicate that the suggested estimator performs better than the MLE in terms of MSE. Then proposed methods are illustrated by a real data analysis.

摘要

大量文献针对解释变量之间存在的多重共线性进行了研究，这些解释变量通常是为了减少对最大似然估计 (MLE) 的不良影响而执行的。特别是，许多作者讨论了均值回归模型框架下的岭估计（RE），因为 RE 具有均方误差（MSE）小于 MLE 的优势。然而，大多数现有方法都假设或适用于对称数据。在本文中，我们考虑了在实践中经常出现的偏斜（或不对称）数据的情况，并将对称数据作为一种特殊情况，并推导了多重共线性问题下偏态正态回归模型的 RE。研究了通过 EM 算法和十一个岭参数方法的最大似然法。蒙特卡洛模拟结果表明，建议的估计器在 MSE 方面比 MLE 表现更好。然后通过实际数据分析说明所提出的方法。