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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 283-296
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\centerline{\large\bf MODEL CHECKING OF DIMENSION-REDUCTION TYPE}
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\centerline{\large\bf FOR REGRESSION}
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\centerline{Li-Xing Zhu}
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\centerline{\it The University of Hong Kong}
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\begin{quotation}
\noindent {\it Abstract:}
Residual analysis is a commonly used technique for  model checking in
regression. However the problem gets more complicated when the dimension of
covariate is high because it is difficult to see what the residuals should be
plotted against. In this paper, we propose a simple search for a good
projection direction for plotting and for constructing a lack-of-fit test.
We also investigate the bootstrap approximation for computing $p$-values.\par
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\noindent {\it Key words and phrases:}
Bootstrap approximation, dimension-reduction,  empirical process, model
checking, residual plot.
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