Tukey Depth-based Multivariate Trimmed Means

Finite Sample Tail Behavior of the Multivariate Trimmed Mean Based on Tukey-Donoho Halfspace Depth

Multi - dimensional trimming based on projection depth

As estimators of location parameters, univariate trimmed means are well-known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy tailed models. This paper introduces multi-dimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investig...

Introduction : The geometry of data

In multivariate analysis, data often cannot be fitted by normal or, more general, elliptically symmetric distributions. Then the classical parametric methodology, which draws on normality or ellipticity, fails. Recently, non-parametric methods have been developed that exploit the geometrical structure of the data in an explicit way and make use of the analyst's geometric intuition. They include...

Multivariate Quantiles and Multiple-output Regression Quantiles: from L1 Optimization to Halfspace Depth

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett’s traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version, those quantiles can be computed efficiently via linear programming techniques. Consistency, Bahadur representation and asymptotic normality results are establ...

Impartial trimmed means for functional data

In this paper we extend the notion of impartial trimming to a functional data framework, and we obtain resistant estimates of the center of a functional distribution. We give mild conditions for the existence and uniqueness of the functional trimmed means. We show the continuity of the population parameter with respect to the weak convergence of probability measures. As a consequence we obtain ...