IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v166y2009i1p339-35310.1007-s10479-008-0412-4.html
   My bibliography  Save this article

Quadratic mixed integer programming and support vectors for deleting outliers in robust regression

Author

Listed:
  • G. Zioutas
  • L. Pitsoulis
  • A. Avramidis

Abstract

We consider the problem of deleting bad influential observations (outliers) in linear regression models. The problem is formulated as a Quadratic Mixed Integer Programming (QMIP) problem, where penalty costs for discarding outliers are used into the objective function. The optimum solution defines a robust regression estimator called penalized trimmed squares (PTS). Due to the high computational complexity of the resulting QMIP problem, the proposed robust procedure is computationally suitable for small sample data. The computational performance and the effectiveness of the new procedure are improved significantly by using the idea of ε-Insensitive loss function from support vectors machine regression. Small errors are ignored, and the mathematical formula gains the sparseness property. The good performance of the ε-Insensitive PTS (IPTS) estimator allows identification of multiple outliers avoiding masking or swamping effects. The computational effectiveness and successful outlier detection of the proposed method is demonstrated via simulated experiments. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • G. Zioutas & L. Pitsoulis & A. Avramidis, 2009. "Quadratic mixed integer programming and support vectors for deleting outliers in robust regression," Annals of Operations Research, Springer, vol. 166(1), pages 339-353, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:339-353:10.1007/s10479-008-0412-4
    DOI: 10.1007/s10479-008-0412-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0412-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0412-4?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. Hawkins, Douglas M., 1994. "The feasible solution algorithm for least trimmed squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 185-196, February.
    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. Mike G. Tsionas, 2021. "Multi-criteria optimization in regression," Annals of Operations Research, Springer, vol. 306(1), pages 7-25, November.
    2. Farnè, Matteo & Vouldis, Angelos T., 2018. "A methodology for automised outlier detection in high-dimensional datasets: an application to euro area banks' supervisory data," Working Paper Series 2171, European Central Bank.
    3. Luca Insolia & Ana Kenney & Francesca Chiaromonte & Giovanni Felici, 2022. "Simultaneous feature selection and outlier detection with optimality guarantees," Biometrics, The International Biometric Society, vol. 78(4), pages 1592-1603, December.
    4. Wang, Yong & Fu, Chengqun & Guo, Jie & Yu, Qin, 2016. "A robust regression based on weighted LSSVM and penalized trimmed squaresAuthor-Name: Liu, Jianyong," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 328-334.
    5. Onur Şeref & Talayeh Razzaghi & Petros Xanthopoulos, 2017. "Weighted relaxed support vector machines," Annals of Operations Research, Springer, vol. 249(1), pages 235-271, February.
    6. Barbato, Michele & Ceselli, Alberto, 2024. "Mathematical programming for simultaneous feature selection and outlier detection under l1 norm," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1070-1084.
    7. Thompson, Ryan, 2022. "Robust subset selection," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    8. C. Chatzinakos & L. Pitsoulis & G. Zioutas, 2016. "Optimization techniques for robust multivariate location and scatter estimation," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1443-1460, May.

    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. Sven Jäger & Anita Schöbel, 2020. "The blockwise coordinate descent method for integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 357-381, April.
    2. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    3. Hawkins, Douglas M., 1995. "Convergence of the feasible solution algorithm for least median of squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 19(5), pages 519-538, May.
    4. Jung, Kang-Mo, 2005. "Multivariate least-trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 307-316, February.
    5. Mount, David M. & Netanyahu, Nathan S. & Piatko, Christine D. & Wu, Angela Y. & Silverman, Ruth, 2016. "A practical approximation algorithm for the LTS estimator," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 148-170.
    6. Atkinson, A. C. & Cheng, Tsung-Chi, 2000. "On robust linear regression with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 33(4), pages 361-380, June.
    7. Agullo, Jose, 2001. "New algorithms for computing the least trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 425-439, June.
    8. Klouda, Karel, 2015. "An exact polynomial time algorithm for computing the least trimmed squares estimate," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 27-40.

    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:annopr:v:166:y:2009:i:1:p:339-353:10.1007/s10479-008-0412-4. 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.