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Sufficient dimension reduction and graphics in regression. (English) Zbl 1047.62066
Summary: 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.

MSC:
62J05 Linear regression; mixed models
62-09 Graphical methods in statistics (MSC2010)
62H99 Multivariate analysis
62J02 General nonlinear regression
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