Theoretical Foundations of Functional Data Analysis, With an Introduction to Linear Operators - Wiley Series in Probability and Statistics

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.

ISBN:	9780470016916
Publisher:	Wiley
Imprint:	John Wiley & Sons, Inc.
Published date:	08 May 2015
DEWEY:	515.7
DEWEY edition:	22
Language:	English
Number of pages:	xiii, 333
Weight:	578g
Height:	238mm
Width:	158mm
Spine width:	24mm

Write a review

Your Name:

Your Review: Note: HTML is not translated!

Rating: Bad           Good

Enter the code in the box below: