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Dimension reduction for the conditional kth moment in regression

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The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the central kth‐moment subspace to capture information from the mean, variance and so on up to the kth conditional moment of the regression. New methods are studied for estimating these subspaces. Connections with sliced inverse regression are established, and examples illustrating the theory are presented.

Keywords: Central subspaces; Dimension reduction subspaces; Permutation tests; Regression graphics; Sliced inverse regression

Document Type: Research Article


Affiliations: 1: University of Georgia, Athens, USA 2: University of Minnesota, St Paul, USA

Publication date: 2002-05-01

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