Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators (Hardcover)

Tailen Hsing

ISBN 10: 0470016914 / ISBN 13: 9780470016916

Published by John Wiley & Sons Inc, New York, 2015

About this Item

Hardcover. 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 selfcontained 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 selfadjoint and non selfadjoint 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. ?? Provides a concise but rigorous account of the theoretical background of FDA. ?? Introduces topics in various areas of mathematics, probability and statistics from the perspective of FDA. ?? Presents a systematic exposition of the fundamental statistical issues in FDA. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780470016916

Bibliographic Details

• Title: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators (Hardcover)
• Publisher: John Wiley & Sons Inc, New York
• Publication Date: 2015
• Language: English
• ISBN 10: 0470016914
• ISBN 13: 9780470016916
• Binding: Hardcover
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

Tailen Hsing Professor, Department of Statistics, University of Michigan, USA. Professor Hsing is a fellow of International Statistical Institute and of the Institute of Mathematical Statistics. He has published numerous papers on subjects ranging from bioinformatics to extreme value theory, functional data analysis, large sample theory and processes with long memory.

Randall Eubank Professor Emeritus, School of Mathematical and Statistical Sciences, Arizona State University, USA. Professor Eubank is well know and respected in the functional data analysis (FDA) field. He has published numerous papers on the subject and is a regular invited speaker at key meetings.