Ley / Verdebout Modern Directional Statistics

1. Auflage 2017
ISBN: 978-1-4987-0666-7
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 190 Seiten

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 Société Française 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 Université 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.

Autoren/Hrsg.

Ley, Christophe

Verdebout, Thomas

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik

Inhaltsverzeichnis

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

Über Autor(innen)

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 Société Française 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 Université 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.