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On the consistency of coordinate-independent sparse estimation with BIC

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  • Zou, Changliang
  • Chen, Xin

Abstract

Chen et al. (2010) [1] propose a unified method–coordinate-independent sparse estimation (CISE)–that is able to simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. However, its attractive features depend on the appropriate choice of the tuning parameter. In this note, we re-examine the Bayesian information criterion (BIC) in sufficient dimension reduction and provide a heuristic derivation. Furthermore, the CISE with BIC is shown to be able to identify the true model consistently.

Suggested Citation

  • Zou, Changliang & Chen, Xin, 2012. "On the consistency of coordinate-independent sparse estimation with BIC," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 248-255.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:248-255
    DOI: 10.1016/j.jmva.2012.04.014
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    References listed on IDEAS

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    1. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    2. Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
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    5. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    6. Zhu, Li-Ping & Zhu, Li-Xing, 2009. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 862-875, May.
    7. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
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    Cited by:

    1. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    2. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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