Open Access
2014 A new concept of quantiles for directional data and the angular Mahalanobis depth
Christophe Ley, Camille Sabbah, Thomas Verdebout
Electron. J. Statist. 8(1): 795-816 (2014). DOI: 10.1214/14-EJS904

Abstract

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.

Citation

Download Citation

Christophe Ley. Camille Sabbah. Thomas Verdebout. "A new concept of quantiles for directional data and the angular Mahalanobis depth." Electron. J. Statist. 8 (1) 795 - 816, 2014. https://doi.org/10.1214/14-EJS904

Information

Published: 2014
First available in Project Euclid: 16 June 2014

zbMATH: 1349.62197
MathSciNet: MR3217789
Digital Object Identifier: 10.1214/14-EJS904

Keywords: Bahadur representation , DD- and QQ-plot , directional statistics , Mahalanobis depth , rotationally symmetric distributions

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
Back to Top