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Dimension reduction for the conditional k th moment in regression
Author(s) -
Yin Xiangrong,
Cook R. Dennis
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00330
Subject(s) - sliced inverse regression , sufficient dimension reduction , linear subspace , dimension (graph theory) , dimensionality reduction , mathematics , subspace topology , moment (physics) , regression , statistics , regression analysis , reduction (mathematics) , econometrics , computer science , artificial intelligence , combinatorics , mathematical analysis , pure mathematics , geometry , physics , classical mechanics
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.