AISM 54, 768-795
© 2002 ISM

Sufficient dimension reduction and graphics in regression

Francesca Chiaromonte1 and R. Dennis Cook2

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.

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