Directional Statistics

Die Statistik gerichteter Daten wird in der zweiten, aktualisierten Auflage dieses Bandes umfassend behandelt - sowohl hinsichtlich der Methodologie als auch der zugrundeliegenden theoretischen Prinzipien. Neu aufgenommen wurde Material zur Regression, Korrelation, zu robusten und Bootstrap-Methoden sowie zur Dichtebestimmung. Mit zahlreichen Anwendungsbeispielen, unter anderem aus der Meteorologie, Biologie, Physik, Astronomie und Bildverarbeitung.

Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work.
The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent material on correlation, regression time series, robust techniques, bootstrap methods, density estimation and curve fitting is presented. The third part considers statistics on more general sample spaces, in particular rotation groups, Stiefel manifolds, Grassmann manifolds and complex projective spaces. Shape analysis is considered from the perspective of directional statistics.
Written by leading authors in the field, this text will be invaluable not only to researchers in probability and statistics interested in the latest developments in directional statistics, but also to practitioners and researchers in many scientific fields, including astronomy, biology, computer vision, earth sciences and image analysis.

"...written as a drastic revision and major extension to Statistics of Directional Data....definitive reference on this subject...for many years." (Short Book Reviews, Vol. 20, No. 3, December 2000) "The text will be an invaluable source of reference for researchers and practitioners alike working with directional data..." (The Statistician, Vol. 50, 2001) "...a highly valuable and nicely written contribution" (Statistics and Decisions, Vol 19/2, 2001)

Auteur

Kantil V. Mardia is a statistician specializing in directional statistics, multivariate analysis, geostatistics, statistical bioinformatics and statistical shape analysis. He was born in Sirohi, Rajasthan, India in a Jain family and now resides and works in Leeds.

Peter E. Jupp is the author of Directional Statistics, published by Wiley.

Contenu

I: Circular data; 2. Summary Statistics; 3 Basic Concepts and Models; 4 Fundamental Theorems and Distribution Theory; 5 Point Estimation; 6 Tests of Uniformity and Tests of Goodness-of-Fit; 7. Tests on von Mises Distributions 8 Non-parametric Methods 9 Distributions on Spheres 10 Inference on Spheres 11 Correlation and Regression 12 Modern Methodology 13 General Sample Spaces 14 Shape Analysis