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ONLINE

Boca Raton, FL : CRC Press, [2017]

1 online zdroj

ISBN 9781315119472 (e-book : PDF)

ISBN 9781351636278 (e-book: Mobi)

ISBN 9781498706643 (vázáno)

Chapman & Hall/CRC interdisciplinary statistics series

"Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory.The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory, high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Societe Francaise de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics.Thomas Verdebout is professor of mathematical statistics at Universite libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high-dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis."--Provided by publisher..

* Sampling (Statistics) * vzorkování

001478467

1 Introduction 1 // 1.1 Overview 1 // 1.1.1 A brief introduction to directional statistics 1 // 1.1.2 A brief outline of the theoretical advances presented in this book 2 // 1.2 Directional datasets 4 // 1.2.1 Paleomagnetism 4 // 1.2.2 Political sciences 6 // 1.2.3 Text mining 6 // 1.2.4 Wildfire orientation 7 // 1.2.5 Life sciences and bioinformatics 8 // 1.3 Basics and notations 10 // 1.4 Plan of the book 12 // 2 Advances in flexible parametric distribution theory 17 // 2.1 Introduction 17 // 2.1.1 Flexible parametric modeling: an active research area onW 17 // 2.1.2 Organization of the remainder of the chapter 18 // 2.2 Flexible circular distributions 18 // 2.2.1 Four ways to construct circular densities 18 // 2.2.2 The classics: von Mises, cardioid and wrapped Cauchy distributions 19 // 2.2.3 Beyond the classics: modern flexible circular modeling 22 // 2.2.4 Flexible modeling of symmetric data: the Jones-Pewsey distribution 22 // 2.2.5 Sine-skewing: a simple tool to skew any symmetric distribution 24 // 2.2.6 Skewness combined with unimodality: the scale-transforming approach 27 // 2.2.7 A general device for building symmetric bipolar distributions 28 // 2.2.8 A brief description of three other flexible models 30 // 2.3 Flexible spherical distributions 35 // 2.3.1 Classical spherical distributions 35 // 2.3.2 Rotationally symmetric distributions 37 // 2.3.3 A general method to skew rotationally symmetric distributions 40 // 2.4 Flexible toroidal and cylindrical distributions 42 // 2.4.1 Some history, motivations and goals 42 // 2.4.2 The bivariate von Mises distribution and its variants 43 // 2.4.3 Mardia-Sutton type cylindrical distributions . 46 // 2.4.4 Johnson-Wehrly type cylindrical distributions 47 // 2.4.5 The copula approach 50 // 2.5 Further reading 52 // 3 Advances in kernel density estimation on directional supports 55 // 3.1 Introduction 55 //

3.1.1 Kernel density estimation on the real line 55 // 3.1.2 Organization of the remainder of the chapter 57 // 3.2 Definitions and main properties 57 // 3.2.1 Spherical kernel density estimation 53 // 3.2.2 Cylindrical kernel density estimation 60 // 3.3 A delicate yet crucial issue: bandwidth choice 61 // 3.3.1 Spherical AMISE and bandwidth selection 61 // 3.3.2 Rule of thumb based on the FvML distribution 63 // 3.3.3 A gain in generality: AMISE via mixtures of FvML densities 64 // 3.3.4 Three further proposals 65 // 3.3.5 Bandwidth selection in the cylindrical setting 66 // 3.4 Inferential procedures 66 // 3.4.1 Non-parametric goodness-of-fit test for directional data 66 // 3.4.2 Non-parametric independence test for cylindrical data 68 // 3.4.3 An overview of non-parametric regression 69 // 3.5 Further reading // 4 Computational and graphical methods // 4.1 Ordering data on the sphere: quantiles and depth functions // 4.1.1 Ordering on R and MP, and organization of the remainder of the section // 4.1.2 Classical depth functions on the sphere // 4.1.3 Projected quantiles and related asymptotic results // 4.1.4 The angular Mahalanobis depth // 4.1.5 Statistical procedures based on projected quantiles and the angular Mahalanobis depth // 4.2 Statistical inference under order restrictions on the circle // 4.2.1 Isotonic regression estimation and organization of the remainder of the section // 4.2.2 Order restrictions on the circle // 4.2.3 Circular isotonic regression // 4.3 Exploring data features with the CircSiZer // 4.3.1 The SiZer, scale space theory and organization of the remainder of the section // 4.3.2 The CircSiZer // 4.3.3 Kernel choice based on causality: the special role of the wrapped normal // 4.4 Computationally fast estimation for high-dimensional FvML distributions //

4.4.1 Maximum likelihood expressions for the parameters of FvML distributions and organization of the section // 4.4.2 Approximations for the concentration parameter from Mardia & Jupp (2000) and their limitations in high dimensions // 4.4.3 New (high-dimensional) approximations for the concentration parameter // 4.5 Further reading // 5 Local asymptotic normality for directional data // 5.1 Introduction // 5.1.1 The LAN property on W and its deep impact on asymptotic statistics // 5.1.2 Organization of the remainder of the chapter // 5.2 Local asymptotic normality and optimal testing // 5.2.1 Contiguity // 5.2.2 Local asymptotic normality // 5.2.3 Optimal testing in LAN experiments // 5.2.4 LAN, semiparametric efficiency and invariance // 5.3 LAN for directional data // 5.3.1 The Le Cam methodology for curved experiments and associated efficient tests // 5.3.2 LAN property for rotationally symmetric distributions // 5.3.3 Application 1: Optimal inference based on signed-ranks // 5.3.4 Application 2: ANOVA on spheres // 5.3.5 Application 3: Asymptotic power of tests of concentration // 5.4 Further reading // 6 Recent results for tests of uniformity and symmetry // 6.1 Introduction // 6.1.1 Organization of the remainder of the chapter // 6.2 Recent advances concerning the Rayleigh test of uniformity // 6.3 Sobolev tests of uniformity // 6.4 Uniformity tests based on random projections // 6.5 Testing for uniformity with noisy data // 6.6 Tests of reflective symmetry on the circle // 6.7 Tests of rotational symmetry on hyperspheres // 6.8 Testing for spherical location in the vicinity of the uniform distribution // 6.9 Further reading // 7 High-dimensional directional statistics // 7.1 Introduction // 7.1.1 High-dimensional techniques in // 7.1.2 Organization of the remainder of the chapter // 7.2 Distributions on high-dimensional spheres //

7.3 Testing uniformity in the high-dimensional case // 7.4 Location tests in the high-dimensional case // 7.5 Concentration tests in the high-dimensional case // 7.6 Principal nested spheres

(OCoLC)993968257