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Original Articles

Detection the symmetry or asymmetry of model errors in partial linear models

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Pages 2217-2234 | Received 08 Jun 2020, Accepted 25 Feb 2021, Published online: 14 Mar 2021
 

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.

Additional information

Funding

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.

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