Modal linear regression models with additive distortion measurement errors

Abstract

We consider modal linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with additive distortion measurement errors. Two calibration procedures are used to estimate parameters in the modal linear regression models, namely, conditional mean calibration and conditional mean calibration with exponential transformation. The asymptotic properties for the estimators based on two calibration procedures are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyze a temperature forecast dataset for an illustration.

Keywords:

• Additive distortion measurement errors
• conditional mean calibration
• exponential transformation
• kernel smoothing

2010 Mathematics Subject Classifications:

• 62G05
• 62G08
• 62G20

Acknowledgements

The authors thank the editor, the associate editor, and two referees for their constructive suggestions that helped us to improve the early manuscript.  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). Yiping Yang's research was supported by the National Social Science Foundation of China (Grant No. 18BTJ035), Chongqing Social Science Planning Project (Grant No. 2019WT58), Chongqing Natural Science Foundation (Grant No. CSTC2020JCYJ-MSXMX0006), Research Fund of Chongqing Technology and Business University (Grant No. 2019ZKYY119) and 2018 Chongqing Statistics Postgraduate Tutor Team (Grant No. YD8 S183002).

Disclosure statement

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