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L1-estimation in linear models with heterogeneous white noise

  • Bantli, Faouzi El
  • Hallin, Marc

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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File URL: http://www.sciencedirect.com/science/article/B6V1D-3XNK6PR-3/2/5bf8b8e15cdafe9aa82772e29c3255f7
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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 45 (1999)
Issue (Month): 4 (December)
Pages: 305-315

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Handle: RePEc:eee:stapro:v:45:y:1999:i:4:p:305-315
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  1. Marc Hallin & Ivan Mizera, 1997. "Unimodality and the asymptotics of M-estimators," ULB Institutional Repository 2013/2217, ULB -- Universite Libre de Bruxelles.
  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. 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.
  4. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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