Staerman, Guillaume

Enthusiasm for Machine Learning is spreading to nearly all fields such as transportation, energy, medicine, banking or insurance as the ubiquity of sensors through IoT makes more and more data at disposal with an ever finer granularity. The abundance of new applications for monitoring of complex infrastructures (e.g. aircrafts, energy networks) tog...

Daouia, Abdelaati Paindaveine, Davy

Despite the importance of expectiles in fields such as econometrics, risk management, and extreme value theory, expectile regression unfortunately remains limited to single-output problems. To improve on this, we define hyperplane-valued multivariate expectiles that show strong advantages over their point-valued competitors. Our expectiles are dire...

Paindaveine, Davy Van Bever, Germain
Published in
Statistical Methods & Applications

We present a discussion of Hubert et al. (2015)—hereafter, HRS15—that splits into two parts. In the first one, we argue that some structural properties of depth may, in some cases, limit its relevance for outlier detection. We also propose an alternative to bagdistances, which, while still based on depth, does not suffer from the same limitations. ...

Dyckerhoff, Rainer Ley, Christophe Paindaveine, Davy
Published in
Annals of the Institute of Statistical Mathematics

McWilliams (J Am Stat Assoc 85:1130–1133, 1990) introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry about the origin (equivalently, about an arbitrary specified center). His procedure first reorders the observations according to their absolute values, then rejects the null when the number of runs in the...

Claeskens, Gerda; 43181; Hubert, Mia; 37727; Slaets, Leen; 55959; Vakili, Kaveh; 74364;

A multivariate depth for functional data is defined and studied. 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. Both population and finite sample versions are studied. The multivariate sample ...

Franco-Pereira, Alba M. Lillo, Rosa E. Romo, Juan
Published in
Lifetime Data Analysis

In this article we present a nonparametric method for constructing confidence bands for the difference of two quantile residual life (qrl) functions. These bands provide evidence for two random variables ordering with respect to the qrl order. The comparison of qrl functions is of importance, specially in the treatment of cancer when there exists a...

Afshani, Peyman Chan, Timothy M.
Published in
Discrete & Computational Geometry

We improve the previous results by Aronov and Har-Peled (SODA’05) and Kaplan and Sharir (SODA’06) and present a randomized data structure of O(n) expected size which can answer 3D approximate halfspace range counting queries in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepac...

Brönnimann, Hervé Lenchner, Jonathan Pach, János
Published in
Graphs and Combinatorics

Given a set S of n points in the plane, the opposite-quadrant depth of a point p∈S is defined as the largest number k such that there are two opposite axis-aligned closed quadrants (NW and SE, or SW and NE) with apex p, each quadrant containing at least k elements of S. We prove that S has a point with opposite-quadrant depth at least n/8. If the e...

Lin, Lu Chen, Minghua
Published in
Statistical Papers

In this paper the estimating equation is constructed via statistical depth. The obtained estimating equation and parameter estimation have desirable robustness, which attain very high breakdown values close to 1/2. At the same time, the obtained parameter estimation still has ordinary asymptotic behaviours such as asymptotic normality. In particula...