Journal
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
Volume 138, Issue 6, Pages 1836-1850Publisher
ELSEVIER
DOI: 10.1016/j.jspi.2007.06.036
Keywords
asymptotic normality; linear regression; median; robustness; super-efficiency
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In this paper, we obtain the strong consistency and asymptotic distribution of the Theil-Sen estimator in simple linear regression models with arbitrary error distributions. We show that the Theil-Sen estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an example in which the Theil-Sen estimator is not asymptotically normal. A small simulation study is conducted to confirm the super-efficiency and the non-normality of the asymptotic distribution. (c) 2007 Elsevier B.V. All rights reserved.
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