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Robust tests for linear regression models based on τ-estimates

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  • Salibian-Barrera, Matias
  • Van Aelst, Stefan
  • Yohai, Víctor J.

Abstract

ANOVA tests are the standard tests to compare nested linear models fitted by least squares. These tests are equivalent to likelihood ratio tests, so they have high power. However, least squares estimators are very vulnerable to outliers in the data, and thus the related ANOVA type tests are also extremely sensitive to outliers. Therefore, robust estimators can be considered to obtain a robust alternative to the ANOVA tests. Regression τ-estimators combine high robustness with high efficiency which makes them suitable for robust inference beyond parameter estimation. Robust likelihood ratio type test statistics based on the τ-estimates of the error scale in the linear model are a natural alternative to the classical ANOVA tests. The higher efficiency of the τ-scale estimates compared with other robust alternatives is expected to yield tests with good power. Their null distribution can be estimated using either an asymptotic approximation or the fast and robust bootstrap. The robustness and power of the resulting robust likelihood ratio type tests for nested linear models is studied.

Suggested Citation

  • Salibian-Barrera, Matias & Van Aelst, Stefan & Yohai, Víctor J., 2016. "Robust tests for linear regression models based on τ-estimates," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 436-455.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:436-455
    DOI: 10.1016/j.csda.2014.09.012
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    References listed on IDEAS

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    1. Samanta, Mayukh & Welsh, A.H., 2013. "Bootstrapping for highly unbalanced clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 70-81.
    2. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
    3. Van Aelst, Stefan & Willems, Gert, 2011. "Robust and Efficient One-Way MANOVA Tests," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 706-718.
    4. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
    5. Salibian-Barrera, Matias & Van Aelst, Stefan & Willems, Gert, 2006. "Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1198-1211, September.
    6. 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.
    7. Nora Muler & Victor J. Yohai, 2002. "Robust estimates for arch processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 341-375, May.
    8. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    9. Wang, Lan & Qu, Annie, 2007. "Robust Tests in Regression Models With Omnibus Alternatives and Bounded Influence," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 347-358, March.
    10. 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.
    11. Salibian-Barrera, Matias & Van Aelst, Stefan, 2008. "Robust model selection using fast and robust bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5121-5135, August.
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