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S-estimation in Linear Models with Structured Covariance Matrices

Author

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  • Ruiz-Gazen, Anne
  • Lopuhaä, Henrik Paul
  • Gares, Valérie

Abstract

We provide a unified approach to S-estimation in balanced linear models with structured covariance matrices. Of main interest are S-estimators for linear mixed effects models, but our approach also includes S-estimators in several other standard multivariate models, such as multiple regression, multivariate regression, and multivariate location and scatter. We provide sufficient conditions for the existence of S-functionals and S-estimators, establish asymptotic properties such as consistency and asymptotic normality, and derive their robustness prop-erties in terms of breakdown point and influence function. All the results are obtained for general identifiable covariance structures and are established under mild conditions on the distribution of the observations, which goes far beyond models with elliptically contoured densities. Some of our results are new and others are more general than existing ones in the literature. In this way this manuscript completes and improves results on S-estimation in a wide variety of multivariate models. We illustrate our results by means of a simulation study and an application to data from a trial on the treatment of lead-exposed children.

Suggested Citation

  • Ruiz-Gazen, Anne & Lopuhaä, Henrik Paul & Gares, Valérie, 2022. "S-estimation in Linear Models with Structured Covariance Matrices," TSE Working Papers 22-1343, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:127042
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    References listed on IDEAS

    as
    1. Copt, Samuel & Victoria-Feser, Maria-Pia, 2006. "High-Breakdown Inference for Mixed Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 292-300, March.
    2. Samuel Copt & Stephane Heritier, 2007. "Robust Alternatives to the F-Test in Mixed Linear Models Based on MM-Estimates," Biometrics, The International Biometric Society, vol. 63(4), pages 1045-1052, December.
    3. Claudio Agostinelli & Víctor J. Yohai, 2016. "Composite Robust Estimators for Linear Mixed Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1764-1774, October.
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