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

Tailen Hsing

ISBN 10: 0470016914 / ISBN 13: 9780470016916

Editore: Wiley Mai 2015, 2015

Riguardo questo articolo

Neuware - 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.

Codice articolo 9780470016916

Dati bibliografici

• Titolo: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
• Editore: Wiley Mai 2015
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 0470016914
• ISBN 13: 9780470016916
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 235 L x 157 A x 24 P (millimetri) 235 millimetri di larghezza per 157 millimetri di altezza per 24 millimetri di profondità
• Peso: 677 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.