Contour Projected Dimension Reduction
The Annals of Statistics, Forthcoming
52 Pages Posted: 24 Dec 2008
Date Written: December 22, 2008
In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace (Cook, 1998b). Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation, and CP-directional regression to estimate the generalized contour subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches, when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.
Keywords: central subspace, central contour subspace, contour projection, directional regression, generalized contour subspace
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