This paper discusses the implications of the decomposition property of the Theil index in sequences of nested and hierarchic grouping structures, formalizing general results applicable to a generic sequence of grouping structures. A specific application to data on wages and employment by industrial classification to measure the evolution of wage inequality through time will be explored, analyzi...

There is a vast literature on robust regression estimators, the bulk of which assumes that the dependent (outcome) variable is continuous. Evidently, there are no published results on the impact of tied values in terms of the Type I error probability. A minor goal in this paper to comment generally on problems created by tied values when testing the hypothesis of a zero slope. Simulations indic...

Changes in vegetation activity are driven by multiple natural and anthropogenic factors, which can be reflected by Normalized Difference Vegetation Index (NDVI) derived from satellites. In this paper, NDVI trends from 1982 to 2012 are first estimated by the Theil–Sen median slope method to explore their spatial and temporal patterns. Then, the impact of climate variables and human activity on t...

We characterize the Theil ordering of income inequality by means of ordinal axioms only.

In this article, we propose the use of the Mahalanobis depth to construct fully affine equivalent Theil-Sen estimators of parameters in a multiple linear model. Our construction includes the spatial depth-based Theil-Sen estimators as a special case. We exhibit that the efficiency of the proposed estimators relative to the least squares estimators increases with the number of parameters under i...

In this article, we propose the Theil-Sen estimators of parameters in a multiple linear regression model based on a multivariate median, generalizing the Theil-Sen estimator in a simple linear regression model. The proposed estimator is shown to be robust, consistent and asymptotically normal under mild conditions, and super-efficient when the error distribution is discontinuous. It can be chos...

Marc A. Willaredt, Kerstin Hasenpusch-Theil, Humphrey Gardner, Igor Kitanovic, Vera Hirschfeld-Warneken, Christian Gojak, Karin Gorgas, C. Lulu Bradford, Joachim Spatz, Stefan Woelfl, Thomas Theil, Kerry L. Tucker 1 Interdisciplinary Center for Neurosciences, University of Heidelberg, Heidelberg, Germany 2 Dept. of Anatomy, University of Heidelberg, Heidelberg, Germany 3 Centres for Neuroscienc...

Marc A. Willaredt, Kerstin Hasenpusch-Theil, Humphrey Gardner, Igor Kitanovic, Vera Hirschfeld-Warneken, Christian Gojak, Karin Gorgas, C. Lulu Bradford, Joachim Spatz, Stefan Woelfl, Thomas Theil, Kerry L. Tucker 1 Interdisciplinary Center for Neurosciences, University of Heidelberg, Heidelberg, Germany 2 Dept. of Anatomy, University of Heidelberg, Heidelberg, Germany 3 Centres for Neuroscienc...