Average derivation estimation with multiplicative distortion measurement errors

Abstract

We consider the average derivation estimation when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Three calibration procedures with several estimation methods are used to estimate the average derivation, namely, conditional mean calibration, conditional absolute mean calibration and conditional variance calibration. The asymptotic properties for the estimators are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators.

Keywords:

• Calibration
• Kernel smoothing
• Multiplicative distortion measurement errors

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 62G05;$·$62G08;$·$62G20

Acknowledgements

The authors thank the editor, the associate editor, and a referee for their constructive suggestions that helped us to improve the early manuscript. Zhenghui Feng’s research was supported by the National Natural Science Foundation of China (Grant No. 11871409). Jun Zhang’s research was supported by the Natural Science Foundation of Guangdong Province (Grant No. 2020A1515010372), and the University stability support program A of Shenzhen (Grant No. 20200813151828003). Baojun Yang (ID: 2019103016) is a senior student majoring in Mathematics and Applied Mathematics at Shenzhen University. This work was done when the third author was supervised by the corresponding author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.