文章基本信息

标题：A new concept of quantiles for directional data and the angular Mahalanobis depth
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作者：Christophe Ley ; Camille Sabbah ; Thomas Verdebout 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2014
卷号：8
期号：1
页码：795-816
DOI：10.1214/14-EJS904
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.