Logarithmic calibration for partial linear models with multiplicative distortion measurement errors

ABSTRACT

In this paper, we propose a new identifiability condition by using the logarithmic calibration for the multiplicative distortion partial linear measurement errors models, when neither the response variable nor the covariates in the parametric part can be directly observed. We propose a logarithmic calibration estimation procedure for the unobserved variables. Then, a profile least squares estimator is proposed, associated with its asymptotic results and confidence intervals construction. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the estimator and test statistic are also established. We employ the smoothly clipped absolute deviation penalty to select relevant variables. Simulation studies demonstrate the performance of the proposed procedure and a real example is analysed to illustrate its practical usage.

KEYWORDS:

• Multiplicative measurement errors
• local linear smoothing
• logarithmic calibration
• restricted estimator
• SCAD

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 62G05
• 62G08
• 62G20

Acknowledgments

The authors thank the editor, the associate editor, and the referee for their constructive suggestions that helped us to improve the early manuscript. Yiping Yang's research was supported by the Social Science Fund of Chongqing (Grant No. 2019WT58) and the Pre-research Project of Chongqing Technology and Business University (Grant No. 2019ZKYYA119). Sanying Feng's research was supported by the National Natural Science Foundation of China (Grant No. 11501522) and also supported by the National Statistical Science Research Project of China (Grant No. 2019LY18).

Disclosure statement

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

ORCID

Jun Zhang  http://orcid.org/0000-0003-4332-5182

Additional information

Funding

Yiping Yang's research was supported by the Social Science Fund of Chongqing [grant number 2019WT58] and the Pre-research Project of Chongqing Technology and Business University [grant number 2019ZKYYA119]. Sanying Feng's research was supported by the National Natural Science Foundation of China [grant number 11501522] and also supported by the National Statistical Science Research Project of China [grant number 2019LY18].