CMStatistics 2015: Start Registration
View Submission - CMStatistics
B0805
Title: Probability integral transforms in directional statistics Authors:  Alfred Kume - University of Kent (United Kingdom)
Peter Jupp - University of St Andrews (United Kingdom) [presenting]
Abstract: The standard method of transforming a continuous distribution on the line to the uniform distribution on the unit interval is the probability integral transform. Such a transform can be defined also for distributions on the circle. A version of probability integral transform is introduced for distributions with continuous positive density on compact Riemannian manifolds (such as spheres or rotation groups). It is a continuous mapping of the manifold to itself that transforms the distribution into the uniform distribution. It is based on the usual probability integral transform along each geodesic through a given point. Although the mapping is not unique, there are `almost canonical' choices. Applications include (i) decomposition of distributions on product spaces into marginal distributions and copulae, (ii) derivation of tests of goodness of fit from tests of uniformity. A non-parametric analogue produces uniform scores, which give rise to multi-sample tests. The construction can be extended to some other sample spaces, including simplices and simply-connected spaces of non-positive curvature.