IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i3p769-798.html
   My bibliography  Save this article

Using sliced mean variance–covariance inverse regression for classification and dimension reduction

Author

Listed:
  • Charles Lindsey
  • Simon Sheather
  • Joseph McKean

Abstract

The sliced mean variance–covariance inverse regression (SMVCIR) algorithm takes grouped multivariate data as input and transforms it to a new coordinate system where the group mean, variance, and covariance differences are more apparent. Other popular algorithms used for performing graphical group discrimination are sliced average variance estimation (SAVE, targetting the same differences but using a different arrangement for variances) and sliced inverse regression (SIR, which targets mean differences). We provide an improved SMVCIR algorithm and create a dimensionality test for the SMVCIR coordinate system. Simulations corroborating our theoretical results and comparing SMVCIR with the other methods are presented. We also provide examples demonstrating the use of SMVCIR and the other methods, in visualization and group discrimination by k-nearest neighbors. The advantages and differences of SMVCIR from SAVE and SIR are shown clearly in these examples and simulation. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Charles Lindsey & Simon Sheather & Joseph McKean, 2014. "Using sliced mean variance–covariance inverse regression for classification and dimension reduction," Computational Statistics, Springer, vol. 29(3), pages 769-798, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:769-798
    DOI: 10.1007/s00180-013-0460-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0460-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-013-0460-3?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. Sheather, Simon J. & McKean, Joseph W. & Crimin, Kimberly, 2008. "Sliced mean variance-covariance inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1908-1927, January.
    2. Bentler, Peter M. & Xie, Jun, 2000. "Corrections to test statistics in principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 381-389, May.
    3. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    4. Cook, R. Dennis & Forzani, Liliana M. & Tomassi, Diego R., 2011. "LDR: A Package for Likelihood-Based Sufficient Dimension Reduction," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i03).
    5. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
    6. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
    Full references (including those not matched with items on IDEAS)

    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. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    2. Artemiou, Andreas & Tian, Lipu, 2015. "Using sliced inverse mean difference for sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 184-190.
    3. Andrea Bergesio & María Eugenia Szretter Noste & Víctor J. Yohai, 2021. "A robust proposal of estimation for the sufficient dimension reduction problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 758-783, September.
    4. repec:jss:jstsof:39:i03 is not listed on IDEAS
    5. 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.
    6. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2022. "Asymptotic and bootstrap tests for subspace dimension," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Cook, R. Dennis & Yin, Xiangrong, 2002. "Asymptotic distributions for testing dimensionality in q-based pHd," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 233-243, July.
    8. Stephen Babos & Andreas Artemiou, 2020. "Sliced inverse median difference regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 937-954, December.
    9. Liu, Xuejing & Huo, Lei & Wen, Xuerong Meggie & Paige, Robert, 2017. "A link-free approach for testing common indices for three or more multi-index models," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 236-245.
    10. François Portier, 2016. "An Empirical Process View of Inverse Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 827-844, September.
    11. Yu, Zhou & Zhu, Lixing & Wen, Xuerong Meggie, 2012. "On model-free conditional coordinate tests for regressions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 61-72.
    12. Schott, James R., 2012. "A note on maximum likelihood estimation for covariance reducing models," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1629-1631.
    13. Orea, Luis & Growitsch, Christian & Jamasb, Tooraj, 2012. "Using Supervised Environmental Composites in Production and Efficiency Analyses: An Application to Norwegian Electricity Networks," Efficiency Series Papers 2012/04, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    14. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 995-1017, December.
    15. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
    16. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    17. Dong, Yuexiao & Yang, Chaozheng & Yu, Zhou, 2016. "On permutation tests for predictor contribution in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 81-91.
    18. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    19. An, Baiguo & Guo, Jianhua & Wang, Hansheng, 2013. "Multivariate regression shrinkage and selection by canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 93-107.
    20. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    21. Portier, François & Delyon, Bernard, 2013. "Optimal transformation: A new approach for covering the central subspace," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 84-107.

    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:spr:compst:v:29:y:2014:i:3:p:769-798. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.