  A new dimension reduction method based on Gaussian finite mixtures is
proposed as an extension to sliced inverse regression (SIR). The model-based
SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e.,
failure in the presence of regression symmetric relationships, without the need
to impose further assumptions. Extensive numerical studies are presented to
compare the new method with some of most popular dimension reduction methods,
such as SIR, sliced average variance estimation, principal Hessian direction,
and directional regression. MSIR appears sufficiently flexible to accommodate
various regression functions, and its performance is comparable with or better,
particularly as sample size grows, than other available methods. Lastly, MSIR
is illustrated with two real data examples about ozone concentration
regression, and hand-written digit classification.
