IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v174y2019ics0047259x19301605.html
   My bibliography  Save this article

Dimension reduction estimation for central mean subspace with missing multivariate response

Author

Listed:
  • Fan, Guo-Liang
  • Xu, Hong-Xia
  • Liang, Han-Ying

Abstract

Multivariate response data often arise in practice and they are frequently subject to missingness. Under this circumstance, the standard sufficient dimension reduction (SDR) methods cannot be used directly. To reduce the dimension and estimate the central mean subspace, a profile least squares estimation method is proposed based on an inverse probability weighted technique. The profile least squares method does not need any distributional assumptions on the covariates and hence differs from existing SDR methods. The resulting estimator of the central mean subspace is proved to be asymptotically normal and root n consistent under some mild conditions. The structural dimension is determined by a BIC-type criterion and the consistency of its estimator is established. Comprehensive simulations and a real data analysis show that the proposed method works promisingly.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jmvana:v:174:y:2019:i:c:s0047259x19301605
    DOI: 10.1016/j.jmva.2019.104542
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X19301605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2019.104542?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. Cheng, Qing & Zhu, Liping, 2017. "On relative efficiency of principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 108-113.
    2. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    3. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    4. Yanyuan Ma & Liping Zhu, 2013. "Efficiency loss and the linearity condition in dimension reduction," Biometrika, Biometrika Trust, vol. 100(2), pages 371-383.
    5. 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.
    6. 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.
    7. 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.
    8. Guo, Xu & Wang, Tao & Xu, Wangli & Zhu, Lixing, 2014. "Dimension reduction with missing response at random," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 228-242.
    9. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    10. Linjun Tang & Zhangong Zhou, 2015. "Weighted local linear CQR for varying-coefficient models with missing covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 583-604, September.
    11. 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.
    12. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    13. 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.
    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. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(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. 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).
    2. Deng, Jianqiu & Yang, Xiaojie & Wang, Qihua, 2022. "Surrogate space based dimension reduction for nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. 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.
    4. Feng, Zhenghui & Wang, Tao & Zhu, Lixing, 2014. "Transformation-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 186-205.
    5. 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.
    6. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    7. 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.
    8. 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.
    9. 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.
    10. Zhou, Jingke & Xu, Wangli & Zhu, Lixing, 2015. "Robust estimating equation-based sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 99-118.
    11. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    12. 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).
    13. Zifang Guo & Lexin Li & Wenbin Lu & Bing Li, 2015. "Groupwise Dimension Reduction via Envelope Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1515-1527, December.
    14. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    15. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.
    16. Qin Wang & Yuan Xue, 2023. "A structured covariance ensemble for sufficient dimension reduction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 777-800, September.
    17. Kim, Kyongwon, 2022. "On principal graphical models with application to gene network," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    18. Feng, Zhenghui & Zhu, Lixing, 2012. "An alternating determination–optimization approach for an additive multi-index model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1981-1993.
    19. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
    20. Cheng, Qing & Zhu, Liping, 2017. "On relative efficiency of principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 108-113.

    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:174:y:2019:i:c:s0047259x19301605. 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.