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Ley, Christophe; Sabbah, Camille; Verdebout, Thomas

A new concept of quantiles for directional data and the angular Mahalanobis depth. (English) Zbl 1349.62197

Electron. J. Stat. 8, No. 1, 795-816 (2014).
Summary: 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.

Cited in 1 Review
Cited in 17 Documents

MSC:

62H11 Directional data; spatial statistics
62G30 Order statistics; empirical distribution functions
62A09 Graphical methods in statistics
62P35 Applications of statistics to physics

Keywords:

Bahadur representation; directional statistics; DD- and QQ-plot; Mahalanobis depth; rotationally symmetric distributions
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Full Text: DOI Euclid

References:

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