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L1-estimation in linear models with heterogeneous white noise

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  • Marc Hallin
  • Faouzi El Bantli

Abstract

Necessary and sufficient conditions are given for the consistency of the L1-estimator of the regression parameter [beta] in linear models with independent but possibly nonidentically distributed errors. The heteroscedastic case is treated as a particular case. The asymptotic normality of is also established, under assumptions which are weaker than in related results on the asymptotics of the sample median in heteroscedastic location models.
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Suggested Citation

  • Marc Hallin & Faouzi El Bantli, 1999. "L1-estimation in linear models with heterogeneous white noise," ULB Institutional Repository 2013/2083, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/2083
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    References listed on IDEAS

    as
    1. Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    2. Marc Hallin & Ivan Mizera, 2001. "Sample heterogeneity and the asymptotics of M-estimators," ULB Institutional Repository 2013/2103, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Ivan Mizera, 1997. "Unimodality and the asymptotics of M-estimators," ULB Institutional Repository 2013/2217, ULB -- Universite Libre de Bruxelles.
    4. Roger W. Koenker & Vasco D'Orey, 1987. "Computing Regression Quantiles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 383-393, November.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    2. Élise, COUDIN & Jean-Marie DUFOUR, 2017. "Finite-Sample Generalized Confidence Distributions and Sign-Based Robust Estimators in Median Regressions with Heterogeneous Dependent Errors," Cahiers de recherche 01-2017, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Qifa Xu & Chao Cai & Cuixia Jiang & Fang Sun & Xue Huang, 2020. "Block average quantile regression for massive dataset," Statistical Papers, Springer, vol. 61(1), pages 141-165, February.

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