Exploring central subspace via contour regression

Contour regression, a method for estimating the central subspace in regression, is based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the central subspace and can be extracted according to two measures of variation in the response: simple and general contour regression (SCR and GCR). When the elliptically contoured distribution and mild assumptions hold, the contour regression approach in comparison with existing sufficient dimension reduction methods suggests exhaustiveness of the central space, keeping n-consistency. In addition, the contour-based approach proves robust to violations of departures from ellipticity. In this paper, two kernel simple and general contour regressions (KSCR and KGCR) are proposed and compared with SCR and GCR.