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?
There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.
I'll point to a couple:
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
Wang, X., X. Dang, H. Peng, and H. Zhang (2009),
The Theil-Sen Estimators in a Multiple Linear Regression Model
The first is based on extending univariate U-quantiles to multivariate U-quantiles, and the second is based on a multivariate median.