SUFFICIENT DIMENSION REDUCTION AND GRAPHICS IN REGRESSION

FRANCESCA CHIAROMONTE^{1} AND R. DENNIS COOK^{2}

1Department of Statistics, Pennsylvania State University, 411 Thomas Building, University Park,

PA, 16802-2111, U.S.A. 2Department of Applied Statistics, School of Statistics, University of Minnesota,

352 Classroom-Office Building, 1994 Buford Avenue, St. Paul, MN 55108-6042, U.S.A.

(Received September 1, 2000; revised July 24, 2001)

Abstract. In this article, we review, consolidate and extend a theory for sufficient dimension reduction in regression settings. This theory provides a powerful context for the construction, characterization and interpretation of low-dimensional displays of the data, and allows us to turn graphics into a consistent and theoretically motivated methodological body. In this spirit, we propose an iterative graphical procedure for estimating the meta-parameter which lies at the core of sufficient dimension reduction; namely, the central dimension-reduction subspace.

Key words and phrases: Sufficient dimension reduction, graphical displays, regression analysis.