\documentclass[10pt]{book}
\usepackage{array}
\textwidth=31.9pc
\textheight=46.5pc
\oddsidemargin=1pc
\evensidemargin=1pc
\headsep=15pt
%\headheight=.2cm
\topmargin=.6cm
\parindent=1.7pc
\parskip=0pt
\def\mbf#1{\mbox{\boldmath $#1$}}
\def\author{\centerline}

\setcounter{page}{1}
\begin{document}
\pagestyle{empty}

\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 601-628

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.121

\vspace{3pc} \normalsize \centerline{\large\bf A UNIFIED VARIABLE
SELECTION APPROACH FOR}

\centerline{\large\bf VARYING COEFFICIENT MODELS} \vspace{.25cm}
\author{Yanlin Tang$^1$, Huixia
Judy Wang$^2$, Zhongyi Zhu$^1$ and Xinyuan Song$^3$} \vspace{.4cm}
\centerline{\it $^1$Fudan University, $^2$North Carolina State
University} \centerline{\it
 and $^3$Chinese University of Hong Kong} \vspace{.55cm}

\begin{quotation}
\noindent {\it Abstract:} In varying coefficient models, three types
of variable selection problems are of practical interests:
separation of varying and constant effects, selection of variables
with nonzero varying effects, and selection of variables with
nonzero constant effects. Existing variable selection methods in the
literature often focus on only one of the three types. In this
paper, we develop a unified variable selection approach for both
least squares regression and quantile regression models with
possibly varying coefficients. The developed method is carried out
by using a two-step iterative procedure based on basis expansion and
a double adaptive-LASSO-type penalty. Under some regularity
conditions, we show that the proposed procedure is consistent in
both variable selection and the separation of varying and constant
coefficients. In addition, the estimated varying coefficients
possess the optimal convergence rate under the same smoothness
assumption, and the estimated constant coefficients have the same
asymptotic distribution as their counterparts obtained when the true
model is known. Finally, we investigate the finite sample
performance of the proposed method through a simulation study and
the analysis of the Childhood Malnutrition Data in India.
\par
\vspace{9pt} \noindent {\it Key words and phrases:} Adaptive LASSO,
B-spline, least squares regression, quantile regression, separation
of varying and constant effects. \par
\end{quotation}
\end{document}
