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

Tailen Hsing | Randall Eubank
€80.99
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A01=Tailen Hsing
Author_Randall Eubank
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Category=PBKF
criminal behavior
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human growth patterns
longitudinal data analysis
Randall Eubank
spatial data analysis
Statistical Analysis of Functional Data
Tailen Hsing

Product details

  • ISBN 9780470016916
  • Weight: 594g
  • Dimensions: 158 x 235mm
  • Publication Date: 08 May 2015
  • Publisher: John Wiley & Sons Inc
  • Publication City/Country: US
  • Product Form: Hardback
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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.
About Randall Eubank | Tailen Hsing
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.

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