Measuring the symmetry of model errors for varying coefficient regression models based on correlation coefficient

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.

Keywords:

• Correlation coefficient
• Empirical likelihood
• Kernel smoothing
• Residuals
• Varying coefficient models

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank the editor, the associate editor and a referee for their constructive suggestions that helped them to improve the early manuscript. Yujie Gai’s research was supported by the National Natural Science Foundation of China (Grant No. 12071497) and National Statistical Science Research Project (Grant No. 2020LY014). Jun Zhang’s research was supported by the Natural Science Foundation of Guangdong Province grant 2020A1515010372.