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September, 1992 Ordering Directional Data: Concepts of Data Depth on Circles and Spheres
Regina Y. Liu, Kesar Singh
Ann. Statist. 20(3): 1468-1484 (September, 1992). DOI: 10.1214/aos/1176348779


Three notions of depth for directional data, angular simplicial depth (ASD), angular Tukey's depth (ATD) and arc distance depth (ADD), are developed and studied. The empirical versions of these depths give rise to center-outward rankings of angular data which may be regarded as extensions of the usual center-outward ranking on the line. Three medians derived from these depths are examined and compared. Applications in nonparametric classification and in implementing the bootstrap to construct confidence regions for directional parameters are briefly discussed.


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Regina Y. Liu. Kesar Singh. "Ordering Directional Data: Concepts of Data Depth on Circles and Spheres." Ann. Statist. 20 (3) 1468 - 1484, September, 1992.


Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0766.62027
MathSciNet: MR1186260
Digital Object Identifier: 10.1214/aos/1176348779

Primary: 62H05
Secondary: 60D05 , 62H12

Keywords: Angular simplicial depth , angular Tukey's depth , arc distance depth , center-outward ordering , directional data , median , von Mises class of distributions

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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