Nonparametric multiplicative distortion measurement errors models with bias reduction

Abstract

In this paper we propose a new nonparametric regression technique under multiplicative distortion measurement errors settings. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. A bias reduction is proposed by choosing a function that is the projection of the unknown regression function onto the parametric family in a certain metric. We find that this new technique leads to substantial improvement in the performance of regression estimators in comparison with the direct one-step estimation, irrespective of the choice of a parametric model. We obtain asymptotic normality results for the estimated nonparametric kernel smoothers, and further discuss their estimation efficiency. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators.

KEYWORDS:

• Bias reduction
• Confounding variable
• Distortion measurement errors
• Kernel smoothing

Acknowledgements

The authors thank the editor, the associate editor and three referees for their constructive suggestions that helped them to 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. 12071305).