IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p4026-4036.html
   My bibliography  Save this article

Simulated annealing for higher dimensional projection depth

Author

Listed:
  • Shao, Wei
  • Zuo, Yijun

Abstract

Data depth for multivariate data has received considerable attention in multivariate nonparametric analysis and robust statistics. Nevertheless, the computation of data depth such as projection depth has remained as a very challenging problem which hinders the development of the projection depth and its wide use in practice. Especially in high dimension, there is no efficient algorithm for the computation of the projection depth and its induced estimators (including the Stahel–Donoho estimator as a special case). In this paper, we employ simulated annealing algorithm by invoking Markov Chain Monte Carlo technique to compute the projection depth. Simulation results show that this new approximate method performs significantly better than its competitors. In lower dimension, we are able to show that the approximate results from this algorithm are very close to the exact ones.

Suggested Citation

  • Shao, Wei & Zuo, Yijun, 2012. "Simulated annealing for higher dimensional projection depth," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4026-4036.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4026-4036
    DOI: 10.1016/j.csda.2012.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312001843
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.05.002?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. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
    2. Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
    3. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
    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. Wei Shao & Yijun Zuo, 2020. "Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm," Computational Statistics, Springer, vol. 35(1), pages 203-226, March.
    2. Dyckerhoff, Rainer & Mozharovskyi, Pavlo & Nagy, Stanislav, 2021. "Approximate computation of projection depths," Computational Statistics & Data Analysis, Elsevier, vol. 157(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. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
    2. Vencalek, Ondrej & Pokotylo, Oleksii, 2018. "Depth-weighted Bayes classification," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 1-12.
    3. Yunlu Jiang & Canhong Wen & Xueqin Wang, 2018. "Adaptive Exponential Power Depth with Application to Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 466-480, October.
    4. Zuo, Yijun, 2021. "Computation of projection regression depth and its induced median," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    5. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
    6. Van Aelst, S. & Vandervieren, E. & Willems, G., 2012. "A Stahel–Donoho estimator based on huberized outlyingness," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 531-542.
    7. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    8. Zuo, Yijun, 2013. "Multidimensional medians and uniqueness," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 82-88.
    9. Wang, Jin, 2019. "Asymptotics of generalized depth-based spread processes and applications," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 363-380.
    10. Francesca Fortunato & Laura Anderlucci & Angela Montanari, 2020. "One‐class classification with application to forensic analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1227-1249, November.
    11. Wei Shao & Yijun Zuo, 2020. "Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm," Computational Statistics, Springer, vol. 35(1), pages 203-226, March.
    12. Dyckerhoff, Rainer & Mozharovskyi, Pavlo & Nagy, Stanislav, 2021. "Approximate computation of projection depths," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    13. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.
    14. Ondrej Vencalek & Olusola Samuel Makinde, 2021. "RR-classifier: a nonparametric classification procedure in multidimensional space based on relative ranks," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 675-693, December.
    15. Prieto, Francisco J., 1997. "Robust covariance matrix estimation and multivariate outlier detection," DES - Working Papers. Statistics and Econometrics. WS 10497, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Liu, Xiaohui & Zuo, Yijun & Wang, Zhizhong, 2013. "Exactly computing bivariate projection depth contours and median," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 1-11.
    17. Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 303-324, April.
    18. Maicol Ochoa & Ignacio Cascos, 2022. "Data Depth and Multiple Output Regression, the Distorted M -Quantiles Approach," Mathematics, MDPI, vol. 10(18), pages 1-19, September.

    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:csdana:v:56:y:2012:i:12:p:4026-4036. 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/locate/csda .

    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.