Logarithmic calibration for nonparametric multiplicative distortion measurement errors models

Abstract

A logarithmic calibration estimation procedure is proposed for nonparametric regression models under the multiplicative distortion measurement errors setting. The unobservable response variable and covariates are both distorted in a multiplicative fashion by an observed confounding variable. By using the logarithmic calibration estimation procedure for unobserved variables, we consider to study the estimates of nonparametric mean function and its first derivative, the variance function, the Sharpe ratio function and correlation curve. We obtain asymptotic normality results for the proposed nonparametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyse a real dataset for an illustration.

Keywords:

• Confounding variable
• errors-in-variables
• logarithmic calibration
• Kernel smoothing

Acknowledgments

The authors thank the editor, the associate editor and the referee for their constructive suggestions that helped them to improve the early manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Xia Cui's work was supported by the National Natural Science Foundation of China [grant number 11871173], and the National Statistical Science Research Project [grant number 2020LZ09].