TITLE:
Estimation of Nonparametric Regression Models with Measurement Error Using Validation Data
AUTHORS:
Fang Liu, Zanhua Yin
KEYWORDS:
Ill-Posed Inverse Problems, Measurement Errors, Nonparametric Regression, Orthogonal Series
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.10,
October
31,
2017
ABSTRACT: We consider the problem of estimating a function g in nonparametric regression
model when only some of covariates are measured with errors with the
assistance of validation data. Without specifying any error model structure
between the surrogate and true covariables, we propose an estimator which
integrates orthogonal series estimation and truncated series approximation
method. Under general regularity conditions, we get the convergence rate of
this estimator. Simulations demonstrate the finite-sample properties of the
new estimator.