Dimension Reduction Regression inR

Dimension Reduction Regression in R

Regression is the study of the dependence of a response variable on a collection predictors collected in . In dimension reduction regression, we seek to find a few linear combinations , such that all the information about the regression is contained in these linear combinations. If is very small, perhaps one or two, then the regression problem can be summarized using simple graphics; for exampl...

Kernel Dimension Reduction in Regression∗

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from the response Y , given the projection of X on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316–342 and Regression Graphics (1998) Wiley]. We show that this conditional independence ass...

Sliced Regression for Dimension Reduction

By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared wit...

Sliced Inverse Regression for Dimension Reduction

Regression on manifolds using kernel dimension reduction

We study the problem of discovering a manifold that best preserves information relevant to a nonlinear regression. Solving this problem involves extending and uniting two threads of research. On the one hand, the literature on sufficient dimension reduction has focused on methods for finding the best linear subspace for nonlinear regression; we extend this to manifolds. On the other hand, the l...