This article defines and studies a depth for multivariate functional data. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape, and phase variation. We study both...

Pareto-type distributions are extreme value distributions for which the extreme value index γ0. Classical estimators for γ0, like the Hill estimator, tend to overestimate this parameter in the presence of outliers. The empirical influence function plot, which displays the influence that each...

Functional data that are not perfectly aligned in the sense of not showing peaks and valleys at the precise same locations possess phase variation. This is commonly addressed by preprocessing the data via a warping procedure. As opposed to treating phase variation as a nuisance effect, it is...

Many univariate robust estimators are based on quantiles. As already theoretically pointed out by Fernholz (in J. Stat. Plan. Inference 57(1), 29–38, <CitationRef CitationID="CR7">1997</CitationRef>), smoothing the empirical distribution function with an appropriate kernel and bandwidth can reduce the variance and mean squared error...</citationref>

Deepest regression (DR) is a method for linear regression introduced by P. J. Rousseeuw and M. Hubert (1999, J. Amer. Statis. Assoc.94, 388-402). The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with...

Motivated by the notion of regression depth (Rousseeuw and Hubert, 1996) we introduce thecatline, a new method for simple linear regression. At any bivariate data setZn={(xi, yi);i=1, ..., n} its regression depth is at leastn/3. This lower bound is attained for data lying on a convex or...

Kernel Based Regression (KBR) minimizes a convex risk over a possibly infinite dimensional reproducing kernel Hilbert space. Recently, it was shown that KBR with a least squares loss function may have some undesirable properties from a robustness point of view: even very small amounts of...