IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v102y2011i9p1280-1292.html
   My bibliography  Save this article

Estimates of MM type for the multivariate linear model

Author

Listed:
  • Kudraszow, Nadia L.
  • Maronna, Ricardo A.

Abstract

We propose a class of robust estimates for multivariate linear models. Based on the approach of MM-estimation (Yohai 1987, [24]), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have both a high breakdown point and high asymptotic efficiency under Gaussian errors. We prove consistency and asymptotic normality assuming errors with an elliptical distribution. We describe an iterative algorithm for the numerical calculation of these estimates. The advantages of the proposed estimates over their competitors are demonstrated through both simulated and real data.

Suggested Citation

  • Kudraszow, Nadia L. & Maronna, Ricardo A., 2011. "Estimates of MM type for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1280-1292, October.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1280-1292
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11000674
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Ben, Marta García & Martínez, Elena & Yohai, Víctor J., 2006. "Robust estimation for the multivariate linear model based on a [tau]-scale," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1600-1622, August.
    2. Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
    3. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    4. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    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. Yani Quarta Mondiana & Henny Pramoedyo & Atiek Iriany & Marjono, 2024. "Exploring Geographical Variability in Sugarcane Yields: A Geographically Weighted Panel Regression Approach with MM Estimation," Advances in Decision Sciences, Asia University, Taiwan, vol. 28(2), pages 35-65, June.
    2. Jorge G. Adrover & Stella M. Donato, 2023. "Aspects of robust canonical correlation analysis, principal components and association," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 623-650, June.
    3. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.
    4. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.

    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. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    2. Nunkesser, Robin & Morell, Oliver, 2008. "Evolutionary algorithms for robust methods," Technical Reports 2008,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    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. Lanius, Vivian & Gather, Ursula, 2010. "Robust online signal extraction from multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 966-975, April.
    5. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2010. "Fast robust estimation of prediction error based on resampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3121-3130, December.
    6. Muler, Nora & Yohai, V´ictor J., 2013. "Robust estimation for vector autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 68-79.
    7. Paindaveine, Davy & Van Bever, Germain, 2014. "Inference on the shape of elliptical distributions based on the MCD," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 125-144.
    8. 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.
    9. Van Aelst, Stefan & Willems, Gert & Zamar, Ruben H., 2013. "Robust and efficient estimation of the residual scale in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 278-296.
    10. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    11. Hofmann, Marc & Kontoghiorghes, Erricos John, 2010. "Matrix strategies for computing the least trimmed squares estimation of the general linear and SUR models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3392-3403, December.
    12. Bernholt, Thorsten & Nunkesser, Robin & Schettlinger, Karen, 2007. "Computing the least quartile difference estimator in the plane," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 763-772, October.
    13. Sirkiä, Seija & Taskinen, Sara & Oja, Hannu, 2007. "Symmetrised M-estimators of multivariate scatter," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1611-1629, September.
    14. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    15. Ian L. Dryden & Gary Walker, 1999. "Highly Resistant Regression and Object Matching," Biometrics, The International Biometric Society, vol. 55(3), pages 820-825, September.
    16. Ma, Yanyuan & Genton, Marc G., 2001. "Highly Robust Estimation of Dispersion Matrices," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 11-36, July.
    17. Serneels, Sven & Verdonck, Tim, 2009. "Principal component regression for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3855-3863, September.
    18. W. Ip & Ying Yang & P. Kwan & Y. Kwan, 2003. "Strong convergence rate of the least median absolute estimator in linear regression models," Statistical Papers, Springer, vol. 44(2), pages 183-201, April.
    19. Nunkesser, Robin & Morell, Oliver, 2010. "An evolutionary algorithm for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3242-3248, December.
    20. Ilmonen, Pauliina, 2013. "On asymptotic properties of the scatter matrix based estimates for complex valued independent component analysis," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1219-1226.

    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:102:y:2011:i:9:p:1280-1292. 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.