IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v112y2012icp248-255.html
   My bibliography  Save this article

On the consistency of coordinate-independent sparse estimation with BIC

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12001054
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2012.04.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    2. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    3. 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.
    4. Lan Wang, 2009. "Wilcoxon-type generalized Bayesian information criterion," Biometrika, Biometrika Trust, vol. 96(1), pages 163-173.
    5. 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.
    6. 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.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li-Ping Zhu & Lin-Yi Qian & Jin-Guan Lin, 2011. "Variable selection in a class of single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1277-1293, December.
    2. Yongjin Li & Qingzhao Zhang & Qihua Wang, 2017. "Penalized estimation equation for an extended single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 169-187, February.
    3. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    4. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    5. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    6. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    7. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    8. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    9. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    10. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.
    11. 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.
    12. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    13. Oguzhan Cepni & I. Ethem Guney & Norman R. Swanson, 2020. "Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 18-36, January.
    14. repec:hum:wpaper:sfb649dp2016-047 is not listed on IDEAS
    15. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    16. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    17. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    18. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    19. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    20. Lee Anthony & Caron Francois & Doucet Arnaud & Holmes Chris, 2012. "Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t Priors," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-31, January.
    21. Ramon I. Garcia & Joseph G. Ibrahim & Hongtu Zhu, 2010. "Variable Selection in the Cox Regression Model with Covariates Missing at Random," Biometrics, The International Biometric Society, vol. 66(1), pages 97-104, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:248-255. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.