Non parametric regression models with additive distortions

Abstract

In this article, we study the non parametric estimation of some regression curves when the data are observed with additive distortions, and these distortions for unobservable response variables and covariates are connected with a common observed confounding variable. We study the estimates of the non parametric mean function and its first derivative, the variance function, the Sharpe ratio function, and the correlation curve function. We obtain asymptotic normality results for the proposed non parametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyze a QSAR fish toxicity dataset for illustration.

Keywords:

• Additive distortion
• confounding variable
• distortion measurement errors
• kernel smoothing
• non parametric regression

Mathematics Subject Classification (2000)::

• 62G05
• 62G08
• 62G20

Acknowledgments

The authors thank the associate editor and two referees for their constructive suggestions that helped them improve the early manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Jun Zhang’s research was supported by the National Natural Science Foundation of China (Grant No.12371448 and Grant No.12071305) and the Science and Technology Planning Project of Shenzhen Municipality, P.R.China (Grant No.20220810155530001). Yujie Gai’s research was supported by the National Natural Science Foundation of China (Grant No. 12071497 and Grant No 12371276), Young Excellence Training Support Program of CUFE(QYP2203), the Emerging Interdisciplinary Project of CUFE and the Central University of Finance and Economics double world-class project construction project. Yiping Yang’s research was supported by the Chongqing Natural Science Foundation (Grant No. cstc2021jcyj-msxmX0079).