Bahadur representation; DD- and QQ-plot; Directional statistics; Mahalanobis depth; Rotationally symmetric distributions; Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] In this paper, we introduce a new concept of quantiles and depth for directional (circular and spherical) data. In view of the similarities with the classical Mahalanobis depth for multivariate data, we call it the angular Mahalanobis depth. Our unique concept combines the advantages of both the depth and quantile settings: appealing depth-based geometric properties of the contours (convexity, nestedness, rotation-equivariance) and typical quantile-asymptotics, namely we establish a Bahadur-type representation and asymptotic normality (these results are corroborated by a Monte Carlo simulation study). We introduce new user-friendly statistical tools such as directional DD- and QQ-plots and a quantile-based goodness- of-fit test. We illustrate the power of our new procedures by analyzing a cosmic rays data set.
Disciplines :
Mathematics
Author, co-author :
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Département de Mathématiques and ECARES, Université Libre de Bruxelles, France
Sabbah, Camille; Laboratoire EQUIPPE, Université Lille Nord de France, France
Verdebout, Thomas; INRIA, Laboratoire EQUIPPE, Université Lille Nord de France, France
External co-authors :
yes
Language :
English
Title :
A new concept of quantiles for directional data and the angular Mahalanobis depth
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