\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



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

\footnotesize
\noindent Statistica Sinica {\bf 12}(2002), 1275-1290
\vspace{3pc} \normalsize

\centerline{\large\bf SENSITIVITY AND OTHER PROPERTIES OF }
\vspace{2pt}
\centerline{\large\bf WAVELET REGRESSION AND DENSITY ESTIMATORS}
\vspace{.25cm}

\centerline{Olivier Renaud}
\vspace{.4cm}
\centerline{\it University of Geneva}
\vspace{.55cm}

\begin{quotation}
\noindent {\it Abstract:}
We give a unified, non-iterative formulation for wavelet estimators
that can be applied in density estimation, regression on a regular
grid and regression with a random design.  This formulation allows
us to better understand the bias due to a given method of
coefficients estimation at high resolution.  We also introduce
functional representations for estimators of interest. The proposed
formulation is well suited for the study of estimation bias and
sensitivity analysis and, in the second part, we compute the
influence function of various wavelet estimators. This tool allows
us to see how the influence of observations can differ strongly
depending on their locations. The lack of shift-invariance can be
investigated and the influence function can be used to compare
different approximation schemes for the wavelet estimator. We show
that a local linear regression-type approximation for the higher
resolution coefficients induces more extreme and variable influence
of the observations on the final estimator than does the standard
approximation.  New approximation schemes are proposed.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Approximation kernel, influence function, irregular design, functional,
sensitivity to the design, shift invariance.\par
\end{quotation}
\end{document}
