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Asymptotics for Least Absolute Deviation Regression Estimators

Published online by Cambridge University Press:  11 February 2009

David Pollard
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Abstract

The LAD estimator of the vector parameter in a linear regression is defined by minimizing the sum of the absolute values of the residuals. This paper provides a direct proof of asymptotic normality for the LAD estimator. The main theorem assumes deterministic carriers. The extension to random carriers includes the case of autoregressions whose error terms have finite second moments. For a first-order autoregression with Cauchy errors the LAD estimator is shown to converge at a 1/n rate.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 186 - 199
Copyright
Copyright © Cambridge University Press 1991

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