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\noindent Statistica Sinica {\bf 13}(2003), 811-826

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\centerline{\large\bf PENALIZED LIKELIHOOD DENSITY ESTIMATION:}
\vspace{2pt}
\centerline{\large\bf DIRECT CROSS-VALIDATION AND SCALABLE}
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\centerline{\large\bf APPROXIMATION}
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\author{Chong Gu and Jingyuan Wang}
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\centerline{\it Purdue University}
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\begin{quotation}
\noindent {\it Abstract:}
For smoothing parameter selection in penalized likelihood density
estimation, a direct cross-validation strategy is illustrated.  The
strategy is as effective as the indirect cross-validation developed
earlier but is much easier to implement in multivariate settings.
Also studied is the practical implementation of certain
low-dimensional approximations of the estimate, with the dimension of
the model space selected to achieve both asymptotic efficiency and
numerical scalability.  The greatly reduced computational burden
allows the routine use of the technique for the analysis of large data
sets.  Related practical issues concerning multivariate numerical
integration are also briefly addressed. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Cross-validation, Kullback-Leibler loss,
penalized likelihood, smoothing parameter.\par
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