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On relative efficiency of principal Hessian directions

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  • Cheng, Qing
  • Zhu, Liping

Abstract

Li (1992) proposed two variants of principal Hessian directions: one is based on centralized response and the other is based on residual of linear regression. We show that the latter has smaller asymptotic variance than the former in quadratic regressions.

Suggested Citation

  • Cheng, Qing & Zhu, Liping, 2017. "On relative efficiency of principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 108-113.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:108-113
    DOI: 10.1016/j.spl.2017.02.030
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    References listed on IDEAS

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    1. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    2. Xia, Yingcun, 2008. "A Multiple-Index Model and Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1631-1640.
    3. Yanyuan Ma & Liping Zhu, 2012. "A Semiparametric Approach to Dimension Reduction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 168-179, March.
    4. Yanyuan Ma & Liping Zhu, 2013. "A Review on Dimension Reduction," International Statistical Review, International Statistical Institute, vol. 81(1), pages 134-150, April.
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    Cited by:

    1. Fan, Guo-Liang & Xu, Hong-Xia & Liang, Han-Ying, 2019. "Dimension reduction estimation for central mean subspace with missing multivariate response," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

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