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Estimates of MM type for the multivariate linear model

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Le Chang & Yanlin Shi, 2024. "A discussion on the robust vector autoregressive models: novel evidence from safe haven assets," Annals of Operations Research, Springer, vol. 339(3), pages 1725-1755, August.
    2. 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.
    3. 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.
    4. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.
    5. 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.

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