Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators:
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Somerset
Wiley
2015
|
| Edition: | 1st ed |
| Series: | Wiley Series in Probability and Statistics
v.997 |
| Subjects: | |
| Summary: | 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 |
| Item Description: | Description based on publisher supplied metadata and other sources |
| Physical Description: | 1 online resource (364 pages) |
| ISBN: | 9781118762561 9780470016916 |
Staff View
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| 520 | |a 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 | ||
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| language | English |
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| spelling | Hsing, Tailen Verfasser aut Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators 1st ed Somerset Wiley 2015 © 2013 1 online resource (364 pages) txt rdacontent c rdamedia cr rdacarrier Wiley Series in Probability and Statistics v.997 Description based on publisher supplied metadata and other sources 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 Functional analysis Linear models (Statistics) Stochastic processes Funktionale Datenanalyse (DE-588)4699227-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s 1\p DE-604 Funktionale Datenanalyse (DE-588)4699227-3 s 2\p DE-604 Eubank, Randall Sonstige oth Erscheint auch als Druck-Ausgabe Hsing, Tailen Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hsing, Tailen Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators Functional analysis Linear models (Statistics) Stochastic processes Funktionale Datenanalyse (DE-588)4699227-3 gnd Linearer Operator (DE-588)4167721-3 gnd |
| subject_GND | (DE-588)4699227-3 (DE-588)4167721-3 |
| title | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_auth | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_exact_search | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_full | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_fullStr | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_full_unstemmed | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_short | Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators |
| title_sort | theoretical foundations of functional data analysis with an introduction to linear operators |
| topic | Functional analysis Linear models (Statistics) Stochastic processes Funktionale Datenanalyse (DE-588)4699227-3 gnd Linearer Operator (DE-588)4167721-3 gnd |
| topic_facet | Functional analysis Linear models (Statistics) Stochastic processes Funktionale Datenanalyse Linearer Operator |
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