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Consistency and asymptotic distribution of the Theil–Sen estimator |
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| Authors: | Hanxiang Peng Shaoli Wang Xueqin Wang |
| Institution: | 1. Department of Mathematics, University of Mississippi, MS 38677-1848, USA;2. Occupational and Environmental Medicine Program, Yale University School of Medicine, New Haven, CT 06510, USA;3. Zhongshan School of Medicine, School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China;4. Department of Epidemiology and Public Health, Yale University, New Haven, CT 06511, USA |
| Abstract: | 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. |
| Keywords: | Asymptotic normality Linear regression Median Robustness Super-efficiency |
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