Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators Hardback
by Tailen (Professor, Department of Statistics, University of Michigan, USA) Hsing, Randall (Professor Emeritus, School of Mathematical and Statistical Sciences, Arizona State Eubank
Part of the Wiley Series in Probability and Statistics series
Hardback
Description
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators.
The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes.
Nonparametric estimation approaches including kernel and regularized smoothing are also introduced.
These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations.
A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA.
It is also suitable for a graduate level special topics course.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:368 pages
- Publisher:John Wiley & Sons Inc
- Publication Date:08/05/2015
- Category:
- ISBN:9780470016916
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:368 pages
- Publisher:John Wiley & Sons Inc
- Publication Date:08/05/2015
- Category:
- ISBN:9780470016916
