A Constructive Approach to the Estimation of Dimension Reduction Directions

Details A Constructive Approach to the Estimation of Dimension Reduction Directions A Constructive Approach to the Estimation of Dimension Reduction Directions

2007-01-26

arxiv.org/abs/math/0701761v1

Mathematics

Statistics Theory

40 pages, 8 figures

Scientific paper

In this paper, we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods (e.g. Li, 1991, 1992; Cook and Weisberg, 1991), the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable, and have better performance than the inverse regression estimation methods for finite samples. Compared with the direct regression estimation methods (e.g. H\"ardle and Stoker, 1989; Hristache, Juditski, Polzehl and Spokoiny, 2001; Xia, Tong, Li and Zhu, 2002), which can only estimate the directions of CS in the regression mean, the new methods can detect the directions of CS exhaustively. Consistency of the estimators and the convergence of corresponding algorithms are proved.

Affiliated with

Also associated with

No associations

Rating

A Constructive Approach to the Estimation of Dimension Reduction Directions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Constructive Approach to the Estimation of Dimension Reduction Directions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Constructive Approach to the Estimation of Dimension Reduction Directions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-568356