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\noindent Statistica Sinica {\bf 15}(2005), 1033-1048

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\centerline{\large\bf TWO-STEP CROSS-VALIDATION SELECTION METHOD}
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\centerline{\large\bf FOR PARTIALLY LINEAR MODELS}
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\author{Panagiotis Avramidis}
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\centerline{\it London School of Economics}
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\begin{quotation}
\noindent {\it Abstract:}
In this article, we deal with the selection of the linear
component and the nonparametric component in a partially linear
model. Our method combines the leave-one-out cross-validation for
the nonparametric component and the leave-$n_v$-out Monte Carlo
Cross Validation (MCCV) for the parametric component. Under some
mild regularity conditions, we show that the estimators are
consistent. Although the results are presented for models
involving the mean regression function, we extend them to include
the variance function while bandwidth selection is discussed
separately. Numerical examples demonstrate the gain in efficiency
using the proposed selection procedure compared to a
fully nonparametric procedure.\par
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\noindent {\it Key words and phrases:}
Bandwidth, cross validation, kernel,
partially linear model, subset selection, Monte Carlo.\par
\end{quotation}

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