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An estimating equation approach to dimension reduction for longitudinal data

Author

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  • Kelin Xu
  • Wensheng Guo
  • Momiao Xiong
  • Liping Zhu
  • Li Jin

Abstract

Sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data. In this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace. The proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified. Even if the covariance structure is misspecified, our estimator remains consistent. In addition, our method relaxes distributional assumptions on the covariates and is doubly robust. To determine the structural dimension of the central mean subspace, we propose a Bayesian-type information criterion. We show that the estimated structural dimension is consistent and that the estimated basis directions are root-$n$ consistent, asymptotically normal and locally efficient. Simulations and an analysis of the Framingham Heart Study data confirm the effectiveness of our approach.

Suggested Citation

  • Kelin Xu & Wensheng Guo & Momiao Xiong & Liping Zhu & Li Jin, 2016. "An estimating equation approach to dimension reduction for longitudinal data," Biometrika, Biometrika Trust, vol. 103(1), pages 189-203.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:189-203.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv066
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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.
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    Cited by:

    1. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    2. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    3. 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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