\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 $#1$}}


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

\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 311-325
\vspace{3pc} \normalsize
\centerline{\large\bf ASYMPTOTIC PROPERTIES OF THE GENERALIZED}
\vspace{2pt}
\centerline{\large\bf SEMI-PARAMETRIC MLE IN LINEAR REGRESSION}
\vspace{.25cm}
\centerline{Qiqing Yu and George Y. C. Wong}
\vspace{.4cm}
\centerline{\it   SUNY, Binghamton
and Strang Cancer Prevention Center}
\vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:}
Consider the semi-parametric linear regression model, $Y=\b^\prime
\bfX+\epsilon$, with sample size $n$, where $\epsilon$ has an unknown cdf
$F_o$. The semi-parametric MLE (SMLE) $\tb_n$ of $\b$ under this set-up,
called the generalized SMLE or GSMLE, has neither been studied in the
literature
nor an algorithm for it. We begin with an algorithm for the GSMLE.
It is then shown that if $F_o$ has a discontinuity point, P$\{\tb_n=\b$ if $n$
is large$\}=1$. Simulation suggests that under some discontinuous
distributions, $\tb_n=\b$ even for $n= 50$.
In contrast the least squares estimator (LSE), $\hat \b_n$, satisfies P$\{ \hat
\b_n \not= \b$ i.o.$\}=1$. We demonstrate via a real discontinuous data
example that the GSMLE can be better than the LSE in applications.
Properties of the GSMLE in the continuous case are also mentioned.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Algorithms, consistency, generalized likelihood, super efficiency.\par
\end{quotation}
\end{document}

