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1999•Canadian Journal of StatisticsOpen access

Asymptotics for L1‐estimators of regression parameters under heteroscedasticityY

Keith Knight

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Abstract

Abstract We consider the asymptotic behaviour of L1 ‐estimators in a linear regression under a very general form of heteroscedasticity. The limiting distributions of the estimators are derived under standard conditions on the design. We also consider the asymptotic behaviour of the bootstrap in the heteroscedastic model and show that it is consistent to first order only if the limiting distribution is normal.

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Abstract We consider the asymptotic behaviour of L1 ‐estimators in a linear regression under a very general form of heteroscedasticity. The limiting distributions of the estimators are derived under standard conditions on the design. We also consider the asymptotic behaviour of the bootstrap in the heteroscedastic model and show that it is consistent to first order only if the limiting distribution is normal.

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Available abstract

Abstract We consider the asymptotic behaviour of L1 ‐estimators in a linear regression under a very general form of heteroscedasticity. The limiting distributions of the estimators are derived under standard conditions on the design. We also consider the asymptotic behaviour of the bootstrap in the heteroscedastic model and show that it is consistent to first order only if the limiting distribution is normal.

Key concepts: Heteroscedasticity, Estimator, Asymptotic distribution, Mathematics, Limiting, Linear regression, Statistics, Regression

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