Contour regression: A general approach to dimension reduction

Details Contour regression: A general approach to dimension reduction Contour regression: A general approach to dimension reduction

2005-08-16

arxiv.org/abs/math/0508277v1

Annals of Statistics 2005, Vol. 33, No. 4, 1580-1616

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000192 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000192

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response, leading to simple and general contour regression (SCR and GCR) methodology. In comparison with existing sufficient dimension reduction techniques, this contour-based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions, while maintaining \sqrtn-consistency and computational ease. Moreover, it proves robust to departures from ellipticity. We establish population properties for both SCR and GCR, and asymptotic properties for SCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal Hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses. We demonstrate the use of contour-based methods on a data set concerning soil evaporation.

Affiliated with

Also associated with

No associations

Rating

Contour regression: A general approach to dimension reduction 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 Contour regression: A general approach to dimension reduction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Contour regression: A general approach to dimension reduction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131478