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Dimension reduction via marginal high moments in regression

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  • Yin, Xiangrong
  • Cook, R. Dennis

Abstract

Yin and Cook [2002. Dimension reduction for the conditional k-th moment in regression. J. Roy. Statist. Soc. B 64, 159-175] established a general equivalence between sliced inverse regression (sir) and a marginal moment method called Covk. In this note, we form a new marginal method called phdk and establish a general equivalence between sliced average variance estimation save, and Covk and phdk. We also show that in the population save is the most comprehensive method among all dimension reduction methods using the first two inverse moments. However, no similar relation was found for dimension reduction methods based on third inverse moments.

Suggested Citation

  • Yin, Xiangrong & Cook, R. Dennis, 2006. "Dimension reduction via marginal high moments in regression," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 393-400, February.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:4:p:393-400
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    References listed on IDEAS

    as
    1. 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.
    2. Xiangrong Yin, 2003. "Estimating central subspaces via inverse third moments," Biometrika, Biometrika Trust, vol. 90(1), pages 113-125, March.
    3. 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.
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