Theoretical foundations of functional data analysis, with an introduction to linear operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Wiley
2015
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| Series: | Wiley Series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 333 S. 229 mm x 152 mm |
| ISBN: | 9780470016916 0470016914 |
Staff View
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Contents Preface xi 1 Introduction 1.1 Multivariate analysis in a nutshell 1.2 The path that lies ahead 1 2 13 2 Vector and function spaces 2.1 Metricspaces 2.2 Vector and normed spaces 2.3 Banach and Lp spaces 2.4 Inner Product and Hilbert spaces 2.5 The projection theorem and orthogonal decomposition 2.6 Vector integrals 2.7 Reproducing kernel Hilbert spaces 2.8 Sobolev spaces 15 16 20 26 31 38 40 46 55 3 Linear operator and functionals 3.1 Operators 3.2 Linear functionals 3.3 Adjoint operator 3.4 Nonnegative, square-root, and projection operators 3.5 Operator inverses 3.6 Fréchet and Gâteaux derivatives 3.7 Generalized Gram-Schmidt decompositions 61 62 66 71 74 77 83 87 4 Compact operators and singular value decomposition 4.1 Compact operators 4.2 Eigenvalues of compact operators 4.3 The singular value decomposition 4.4 Hilbert-Schmidt operators 4.5 Trace class operators 91 92 96 103 107 113
CONTENTS viii 4.6 4.7 4.8 Integral operators and Mercer’s Theorem 116 Operators on an RKHS 123 Simultaneous diagonalization of two nonnegative definite operators 126 5 Perturbation theory 5.1 Perturbation of self-adjoint compact operators 5.2 Perturbation of general compact operators 129 129 140 6 Smoothing and regularization 6.1 Functional linear model 6.2 Penalized least squares estimators 6.3 Bias and variance 6.4 A computational formula 6.5 Regularization parameter selection 6.6 Splines 147 147 150 157 158 161 165 7 Random elements in a Hilbert space 7.1 Probability measures on a Hilbert space 7.2 Mean and covariance of a random element of a Hilbert space 7.3 Mean-square continuous processes and the Karhunen-Lòeve Theorem 184 7.4 Mean-square continuous processes in L2(E, ՑՏ(E), μ) 7.5 RKHS valued processes 7.6 The closed span of a process 7.7 Large sample theory 175 176 178 190 195 198 203 8 Mean and covariance estimation 8.1 Sample mean and covariance operator 8.2 Local linear estimation 8.3 Penalized least-squares estimation 211 212 214 231 9 Principal components analysis 9.1 Estimation via the sample covariance operator 9.2 Estimation via local linear smoothing 9.3 Estimation via penalized least squares 251 253 255 261 10 Canonical correlation analysis 10.1 CCA for random elements of a Hilbert space 10.2 Estimation 10.3 Prediction and regression 265 267 274 281
CONTENTS 10.4 Factor analysis 10.5 MANOVA and discriminant analysis 10.6 Orthogonal subspaces and partial cca 11 Regression 11.1 11.2 11.3 11.4 A functional regression model Asymptotic theory Minimax optimality Discretely sampled data ix 284 288 294 305 305 308 318 321 References 327 Index 331 Notation Index 334 |
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| physical | XIII, 333 S. 229 mm x 152 mm |
| publishDate | 2015 |
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| publisher | Wiley |
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| series2 | Wiley Series in probability and statistics |
| spelling | Hsing, Tailen Verfasser (DE-588)1113612231 aut Theoretical foundations of functional data analysis, with an introduction to linear operators Tailen Hsing ; Randall Eubank New York, NY Wiley 2015 XIII, 333 S. 229 mm x 152 mm txt rdacontent n rdamedia nc rdacarrier Wiley Series in probability and statistics Linearer Operator (DE-588)4167721-3 gnd rswk-swf Funktionale Datenanalyse (DE-588)4699227-3 gnd rswk-swf Biometrie Datenanalyse Regressionsanalyse Funktionale Datenanalyse (DE-588)4699227-3 s DE-604 Linearer Operator (DE-588)4167721-3 s Eubank, Randall L. 1952- Verfasser (DE-588)132752220 aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5164414&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027943020&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsing, Tailen Eubank, Randall L. 1952- Theoretical foundations of functional data analysis, with an introduction to linear operators Linearer Operator (DE-588)4167721-3 gnd Funktionale Datenanalyse (DE-588)4699227-3 gnd |
| subject_GND | (DE-588)4167721-3 (DE-588)4699227-3 |
| 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 Tailen Hsing ; Randall Eubank |
| title_fullStr | Theoretical foundations of functional data analysis, with an introduction to linear operators Tailen Hsing ; Randall Eubank |
| title_full_unstemmed | Theoretical foundations of functional data analysis, with an introduction to linear operators Tailen Hsing ; Randall Eubank |
| 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 | Linearer Operator (DE-588)4167721-3 gnd Funktionale Datenanalyse (DE-588)4699227-3 gnd |
| topic_facet | Linearer Operator Funktionale Datenanalyse |
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