Pepe, M.S. and Fleming, T.R. (1991) A General Nonparametric Method for Dealing with Errors in Missing or Surrogate Covaraite Data. Journal of the American Statistical Association, 86, 108-113.
http://dx.doi.org/10.1080/01621459.1991.10475009

has been cited by the following article:

• TITLE: Estimation of Nonparametric Multiple Regression Measurement Error Models with Validation Data

  AUTHORS: Zanhua Yin, Fang Liu

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

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.7, December 30, 2015

  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.