Estimation of Nonparametric Multiple Regression Measurement Error Models with Validation Data

Zanhua Yin, Fang Liu

College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China.

DOI: 10.4236/ojs.2015.57080                

Abstract

In this article, we develop estimation approaches for nonparametric multiple regression measurement error models when both independent validation data on covariables and primary data on the response variable and surrogate covariables are available. An estimator which integrates Fourier series estimation and truncated series approximation methods is derived without any error model structure assumption between the true covariables and surrogate variables. Most importantly, our proposed methodology can be readily extended to the case that only some of covariates are measured with errors with the assistance of validation data. Under mild conditions, we derive the convergence rates of the proposed estimators. The finite-sample properties of the estimators are investigated through simulation studies.

Keywords

Ill-Posed Inverse Problem, Linear Operator, Measurement Errors, Nonparametric Regression, Validation Data

Conflicts of Interest

The authors declare no conflicts of interest.

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