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Bootstrapping MM-estimators for linear regression with fixed designs

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  • Salibian-Barrera, Matias

Abstract

In this paper, I study the extension of the robust bootstrap [Salibian-Barrera, M., Zamar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582] to the case of fixed designs. The robust bootstrap is a computer-intensive inference method for robust regression estimators which is computationally simple (because we do not need to re-compute the robust estimate with each bootstrap sample) and robust to the presence of outliers in the bootstrap samples. In this paper, I prove the consistency of this method for the case of non-random explanatory variables and illustrate its use on a real data set. Simulation results indicate that confidence intervals based on the robust bootstrap have good finite-sample coverage levels.

Suggested Citation

  • Salibian-Barrera, Matias, 2006. "Bootstrapping MM-estimators for linear regression with fixed designs," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1287-1297, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1287-1297
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    References listed on IDEAS

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    1. Jun Shao, 1990. "Bootstrap estimation of the asymptotic variances of statistical functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 737-752, December.
    2. Shao, Jun, 1992. "Bootstrap variance estimators with truncation," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 95-101, September.
    3. Parr, William C., 1985. "The bootstrap: Some large sample theory and connections with robustness," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 97-100, April.
    4. Matias Salibian-Barrera, 2006. "The Asymptotics of MM-Estimators for Linear Regression with Fixed Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(3), pages 283-294, June.
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    Cited by:

    1. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    2. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Discussion Paper 2006-50, Tilburg University, Center for Economic Research.
    3. Camponovo, Lorenzo & Scaillet, Olivier & Trojani, Fabio, 2012. "Robust subsampling," Journal of Econometrics, Elsevier, vol. 167(1), pages 197-210.

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