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On estimation efficiency of the central mean subspace

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  • Yanyuan Ma
  • Liping Zhu

Abstract

type="main" xml:id="rssb12044-abs-0001"> We investigate the estimation efficiency of the central mean subspace in the framework of sufficient dimension reduction. We derive the semiparametric efficient score and study its practical applicability. Despite the difficulty caused by the potential high dimension issue in the variance component, we show that locally efficient estimators can be constructed in practice. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance and gain in efficiency of the proposed estimators in comparison with several existing methods.

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  • Yanyuan Ma & Liping Zhu, 2014. "On estimation efficiency of the central mean subspace," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 885-901, November.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:5:p:885-901
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.76.issue-5
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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).
    2. Luo, Wei & Cai, Xizhen, 2016. "A new estimator for efficient dimension reduction in regression," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 236-249.
    3. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Xinchao Luo & Lixing Zhu & Hongtu Zhu, 2016. "Single‐index varying coefficient model for functional responses," Biometrics, The International Biometric Society, vol. 72(4), pages 1275-1284, December.
    5. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    6. Jared D. Huling & Menggang Yu, 2022. "Sufficient dimension reduction for populations with structured heterogeneity," Biometrics, The International Biometric Society, vol. 78(4), pages 1626-1638, December.
    7. Chen, Fei & Shi, Lei & Zhu, Xuehu & Zhu, Lixing, 2018. "Generalized principal Hessian directions for mixture multivariate skew elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 142-159.
    8. Zhang, Yaowu & Zhu, Liping & Ma, Yanyuan, 2017. "Efficient dimension reduction for multivariate response data," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 187-199.
    9. Zhu, Liping & Zhong, Wei, 2015. "Estimation and inference on central mean subspace for multivariate response data," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 68-83.

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