Abstract

In this paper, we propose a residuals based estimator of k-th correlation coefficient between the density function and distribution function for varying coefficient regression models, and further we use this k-th correlation coefficient to test whether the density function of the true model error is symmetric or not. First, we propose a moment based estimator of k-th correlation coefficient and present its asymptotic results. Second, we consider statistical inference of k-th correlation coefficient by using the empirical likelihood method, and the empirical likelihood statistic is shown to be asymptotically distributed as Chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators, and we also use our proposed estimators to analyze the CEO dataset.

摘要

在本文中，我们针对变系数回归模型提出了一种基于残差的密度函数和分布函数之间的第k个相关系数估计器，并进一步使用这个第k个相关系数来检验密度函数是否真实模型的误差是否对称。首先，我们提出了一个基于矩的k相关系数估计量，并给出了它的渐近结果。其次，我们考虑k的统计推断-th 相关系数通过使用经验似然法，并且经验似然统计显示为渐近分布为卡方。进行模拟研究以检查提议的估计器的性能，我们还使用我们提议的估计器来分析 CEO 数据集。