Unbiasedness of the Theil-Sen Estimator
Document Type
Lecture
Publication Date
10-23-2003
Abstract
In this talk, we shall introduce the Theil-Sen estimator in a simple linear regression model. It has many nice properties, which could be found in several classical textbooks on nonparametric statistics (see, e.g., Sprent (1993) and Hollander and Wolfe (1973 and 1999)). Sen (1968) claimed that the Theil-Sen estimator is symmetric and unbiased under the assumption that the error distribution is continuous. The statement is incorrect. Weconstruct several counterexamples. Furthermore, we show that the continuity assumption on the error distribution is not important to unbiasedness. In particular, if the sample size n =2or3,thentheTheil-Sen estimator is unbiased. Moreover, if either the error distribution or the covariates have certain symmetry, then the Theil-Sen estimator is also unbiased.
Relational Format
presentation
Recommended Citation
Wang, Xueqin, "Unbiasedness of the Theil-Sen Estimator" (2003). Probability & Statistics Seminar. 65.
https://egrove.olemiss.edu/math_statistics/65
