Modern Directional Statistics

Introduction Overview Directional data sets Basics and notations Plan of the book Advances in flexible parametric distribution theory Introduction Flexible circular distributions Flexible spherical distributions Flexible toroidal and cylindrical distributions Further reading Advances in kernel density estimation on directional supports Introduction Definitions and main properties A delicate yet crucial issue: bandwidth choice Bandwidth selection in the cylindrical setting Inferential procedures Further reading Computational and graphical methods Ordering data on the sphere: quantiles and depth functions Statistical inference under order restrictions on the circle Computationally fast estimation for high-dimensional FvML distributions New (high -dimensional) approximations for the concentration parameter Further reading Local asymptotic normality for directional data Introduction Local asymptotic normality and optimal testing LAN for directional data Further reading Recent results for tests of uniformity and symmetry Introduction Recent advances concerning the Rayleigh test of uniformity Sobolev tests of uniformity Uniformity tests based on random projections Testing for uniformity with noisy data Tests of reflective symmetry on the circle Tests of rotational symmetry on hyperspheres Testing for spherical location in the vicinity of the uniform distribution Further reading High-dimensional directional statistics Introduction Distributions on high-dimensional spheres Testing uniformity in the high-dimensional case Location tests in the high-dimensional case Concentration tests in the high-dimensional case Principal nested spheres Further reading