Dimension reduction for non-elliptically distributed predictors: second-order methods.

YUEXIAO DONG; BING LI

Many classical dimension reduction methods, especially those based on inverse conditional moments, require the predictors to have elliptical distributions, or at least to satisfy a linearity condition. Such conditions, however, are too strong for some applications. Li and Dong (2009) introduced the notion of the central solution space and used it to modify first-order methods, such as sliced inverse regression, so that they no longer rely on these conditions. In this paper we generalize this idea to second-order methods, such as sliced average variance estimation and directional regression. In doing so we demonstrate that the central solution space is a versatile framework: we can use it to modify essentially all inverse conditional moment-based methods to relax the distributional assumption on the predictors. Simulation studies and an application show a substantial improvement of the modified methods over their classical counterparts.

NEWTON-Raphson method; REGRESSION analysis; INVERSE problems; ELLIPTIC differential equations; DIMENSION reduction (Statistics)

Biometrika, 2010, Vol 97, Issue 2, p279

0006-3444

Academic Journal

10.1093/biomet/asq016