Abstract

In this paper, we propose a k-th correlation coefficient estimator between the density function and distribution function of the model errors in single-index models and partial linear single-models. This k-th correlation coefficient estimator is used 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 the k-th correlation coefficient estimator by using the empirical likelihood method. The empirical likelihood statistic is shown to be asymptotically distributed a centered chi-squared distribution with degree of freedom one. Simulation studies are conducted to examine the performance of the proposed estimators and test statistics.

摘要

在本文中，我们提出了单指标模型和部分线性单模型中模型误差的密度函数和分布函数之间的第k个相关系数估计量。这个第k个相关系数估计器用于检验真实模型误差的密度函数是否对称。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 相关系数估计器，使用经验似然法。经验似然统计量显示为渐近分布的中心卡方分布，自由度为 1。进行模拟研究以检查建议的估计器和测试统计数据的性能。