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\noindent Statistica Sinica {\bf 13}(2003), 297-310
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\centerline{\large\bf AN ASYMPTOTIC THEORY FOR SIR$_{\mbf{\alpha}}$ METHOD}
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\centerline{Ali Gannoun and J\'er\^ome Saracco}
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\centerline{\it Universit\'e Montpellier II}
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\begin{quotation}
\noindent {\it Abstract:}
Sliced Inverse Regression (SIR) is a nonparametric method for achieving
dimension reduction in regression problems. It is widely applicable, very
easy to implement on a computer and requires no nonparametric smoothing
devices such as kernel regression or smoothing splines regression.
The first moment-based SIR has been extensively studied. However,
one major restriction is its vulnerability to symmetric dependencies.
Methods based on second moments have been suggested as a remedy, one
is called SIR$_\alpha$. In this paper, we establish the asymptotic
normality of the SIR$_\alpha$ estimates.\par
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\noindent {\it Key words and phrases:}
Asymptotics, eigen-elements, semiparametric regression model, sliced inverse
regression (SIR).
\end{quotation}
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