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Dimension reduction for the conditional kth moment via central solution space

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  • Dong, Yuexiao
  • Yu, Zhou

Abstract

Sufficient dimension reduction aims at finding transformations of predictor X without losing any regression information of Y versus X. If we are only interested in the information contained in the mean function or the kth moment function of Y given X, estimation of the central mean space or the central kth moment space becomes our focus. However, existing estimators for the central mean space and the central kth moment space require a linearity assumption on the predictor distribution. In this paper, we relax this stringent assumption via the notion of central kth moment solution space. Simulation studies and analysis of the Massachusetts college data set confirm that our proposed estimators of the central kth moment space outperform existing methods for non-elliptically distributed predictors.

Suggested Citation

  • Dong, Yuexiao & Yu, Zhou, 2012. "Dimension reduction for the conditional kth moment via central solution space," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 207-218.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:207-218
    DOI: 10.1016/j.jmva.2012.06.001
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    References listed on IDEAS

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    1. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    2. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
    3. 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.
    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    5. Yuexiao Dong & Bing Li, 2010. "Dimension reduction for non-elliptically distributed predictors: second-order methods," Biometrika, Biometrika Trust, vol. 97(2), pages 279-294.
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