Journal
JOURNAL OF NONPARAMETRIC STATISTICS
Volume 17, Issue 1, Pages 107-120Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/1048525042000267743
Keywords
strong consistency; asymptotic normality; non-parametric statistics; linear regression
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We consider a simple linear regression model. The Theil-Sen estimator (TSE) is a point estimator of the slope parameter in the model and has many nice properties, including asymptotic normality. Thus, it has been introduced in several classical textbooks on non-parametric statistics. Most of its properties are established under the assumptions that the error distribution is absolutely continuous and the covariate is not random. In this paper, we study asymptotic properties of the TSE in a simple linear regression model with a random covariate and an arbitrary error distribution, which may not be continuous. We show that it is strongly consistent and has an asymptotic distribution, which may not be a normal distribution if the error distribution is not absolutely continuous.
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