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Dimension reduction for the conditional kth moment in regression

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  • Xiangrong Yin
  • R. Dennis Cook

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 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.

Suggested Citation

  • Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:159-175
    DOI: 10.1111/1467-9868.00330
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    References listed on IDEAS

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    1. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    2. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
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