Model-based SIR for dimension reduction

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)1 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 the 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.

► A new dimension reduction method, called MSIR, for regression problems based on Gaussian finite mixtures is proposed.
► An algorithm for MSIR estimation is described, its consistency and accuracy discussed. The problem of dimensionality is also addressed.
► The method appears sufficiently flexible to accommodate various regression functions, including symmetric relationships and correlated predictors.
► MSIR performance is comparable with or better, particularly as sample size grows, than other available methods.