Abstract
In this paper, we propose a residual-based estimator of k-th correlation coefficient between the density function and distribution function of a continuous variable for partial linear 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.
Acknowledgements
The authors thank the associate editor and two referees for their constructive suggestions that helped them to improve the early manuscript.