Dimension reduction for the conditional kth moment in regression |
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Authors: | Xiangrong Yin & R Dennis Cook |
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Institution: | University of Georgia, Athens, USA,;University of Minnesota, St Paul, USA |
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Abstract: | 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 k th-moment subspace to capture information from the mean, variance and so on up to the k th 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. |
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Keywords: | Central subspaces Dimension reduction subspaces Permutation tests Regression graphics Sliced inverse regression |
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