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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1093-1113

\vspace{3pc} \normalsize \centerline{\large\bf NONPARAMETRIC
REGRESSION FUNCTION ESTIMATION} \vspace{2pt} \centerline{\large\bf
FOR ERRORS-IN-VARIABLES MODELS} \vspace{2pt} \centerline{\large\bf
WITH VALIDATION DATA} \vspace{.25cm}
\author{Lilun Du, Changliang Zou and  Zhaojun
Wang} \vspace{.4cm} \centerline{\it Nankai University}
\vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} This paper develops an estimation approach
for nonparametric regression analysis with measurement error in
covariates, assuming the availability of independent validation data
on them, in addition to primary data on the response variable and
surrogate covariates. Without specifying any error model structure
between the surrogate and true covariates,  we propose an estimator
that integrates local linear regression and Fourier transformation
methods. Under mild conditions, the consistency of the proposed
estimator is established and the convergence rate is also obtained.
Numerical examples show that it performs well in applications.\par
\vspace{9pt} \noindent {\it Key words and phrases:} Asymptotic
normality, local linear regression, measurement error, trigonometric
series. \par
\end{quotation}

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