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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 575-599

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.105

\vspace{3pc} \normalsize \centerline{\large\bf ADAPTIVE SEMI-VARYING
COEFFICIENT MODEL} \vspace{2pt} \centerline{\large\bf  SELECTION}
\vspace{.25cm}
\author{Tao Hu$^{1,2}$ and Yingcun Xia$^3$}
\vspace{.4cm} \centerline{\it $^1$Guizhou College of Finance and
Economics, $^2$Capital Normal University} \centerline{\it
 and $^3$National University of Singapore} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} Identification of constant coefficients in
a semi-varying coefficient model is an important issue (Zhang et al
(2002)).
 We propose a novel method   for this  by combining local polynomial smoothing
  (Fan and Zhang (1999))
  with shrinkage estimation (Tibshirani (1996)).
   Unlike the stepwise procedure (Xia et al (2004)),
    our method can
identify the constant coefficients and estimate the model
simultaneously. By imposing the adaptive LASSO penalty and starting
with  the Nadaraya-Watson estimator, the method can identify the
constant coefficients and varying coefficients consistently, and
estimate the model with oracle efficiency  (Fan and Li (2001)).
\par \vspace{9pt} \noindent {\it Key words and phrases:}
BIC, kernel smoothing, LASSO, model selection,  oracle property,
SCAD, semi-varying coefficient model. \par
\end{quotation}

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