TITLE:
Nonparametric Regression Estimation with Mixed Measurement Errors
AUTHORS:
Zanhua Yin, Fang Liu, Yuanfu Xie
KEYWORDS:
Berkson Error, Classical Error, Deconvolution, Kernel Method, Mixed Measurement Errors
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.17,
November
30,
2016
ABSTRACT: We consider the estimation of nonparametric
regression models with predictors being measured with a mixture of Berkson and
classical errors. In practice, the Berkson error arises when the variable X of
interest is unobservable and only a proxy of X can be measured while the
inaccuracy related to the observation of the proxy causes an error of classical
type. In this paper, we propose two nonparametric estimators of the regression
function in the presence of either or both types of errors. We prove the asymptotic
normality of our estimators and derive their rates of convergence. The
finite-sample properties of the estimators are investigated through simulation
studies.