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Is the Theil-Sen estimation in robust regression only limited to a two dimensional problem or can you use it for more than one independent variable as well?

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  • $\begingroup$ no, it's only limited to two dimensional problems. There are many, much better alternative though and those generalize trivially to higher dimensions (search for robust regression here). $\endgroup$ – user603 May 3 '14 at 14:10
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There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.

I'll point to a couple:

1)

Zhou, W. and R. Serfling (2007),
Multivariate Spatial U-Quantiles: a Bahadur-Kiefer Representation, a Theil-Sen Estimator for Multiple Regression, and a Robust Dispersion Estimator,
Journal of Statistical Planning and Inference, May

see here


2)

Wang, X., X. Dang, H. Peng, and H. Zhang (2009),
The Theil-Sen Estimators in a Multiple Linear Regression Model

see here or here (different versions)


The first is based on extending univariate U-quantiles to multivariate U-quantiles, and the second is based on a multivariate median.

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