Wavelets, approximation and statistical applications:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Lecture notes in statistics
129 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 265 S. Ill., graph. Darst. |
| ISBN: | 0387984534 |
Staff View
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| 245 | 1 | 0 | |a Wavelets, approximation and statistical applications |c Wolfgang Härdle ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XIII, 265 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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| adam_text | Contents
Preface v
List of Figures xi
List of Tables xv
Symbols and Notation xvii
1 Wavelets 1
1.1 What can wavelets offer? 1
1.2 General remarks 7
1.3 Data compression 8
1.4 Local adaptivity 13
1.5 Nonlinear smoothing properties 15
1.6 Synopsis 15
2 The Haar basis wavelet system 17
3 The idea of multiresolution analysis 25
3.1 Multiresolution analysis 25
3.2 Wavelet system construction 27
3.3 An example 29
4 Some facts from Fourier analysis 31
vii
viii CONTENTS
5 Basic relations of wavelet theory 35
5.1 When do we have a wavelet expansion? 35
5.2 How to construct mothers from a father 42
5.3 Additional remarks 44
6 Construction of wavelet bases 47
6.1 Construction starting from Riesz bases 47
6.2 Construction starting from m0 54
7 Compactly supported wavelets 59
7.1 Daubechies construction 59
7.2 Coiflets 63
7.3 Symmlets 66
8 Wavelets and Approximation 71
8.1 Introduction 71
8.2 Sobolev Spaces 72
8.3 Approximation kernels 75
8.4 Approximation theorem in Sobolev spaces 76
8.5 Periodic kernels and projection operators 81
8.6 Moment condition for projection kernels 84
8.7 Moment condition in the wavelet case 90
9 Wavelets and Besov Spaces 101
9.1 Introduction 101
9.2 Besov spaces 101
9.3 Littlewood Paley decomposition 106
9.4 Approximation theorem in Besov spaces 116
9.5 Wavelets and approximation in Besov spaces 117
10 Statistical estimation using wavelets 125
10.1 Introduction 125
10.2 Linear wavelet density estimation 126
10.3 Soft and hard thresholding 138
10.4 Linear versus nonlinear wavelet density estimation 146
10.5 Asymptotic properties of wavelet thresholding estimates . . . 163
10.6 Some real data examples 171
CONTENTS ix
10.7 Comparison with kernel estimates 176
10.8 Regression estimation 183
10.9 Other statistical models 188
11 Wavelet thresholding and adaptation 193
11.1 Introduction 193
11.2 Different forms of wavelet thresholding 193
11.3 Adaptivity properties of wavelet estimates 198
11.4 Thresholding in sequence space 201
11.5 Adaptive thresholding and Stein s principle 205
11.6 Oracle inequalities 210
11.7 Bibliographic remarks 212
12 Computational aspects and software 215
12.1 Introduction 215
12.2 The cascade algorithm 216
12.3 Discrete wavelet transform 220
12.4 Statistical implementation of the DWT 222
12.5 Translation invariant wavelet estimation 228
12.6 Main wavelet commands in XploRe 231
A Tables 237
A.I Wavelet Coefficients 237
A.2 239
B Software Availability 240
C Bernstein and Rosenthal inequalities 241
D A Lemma on the Riesz basis 246
Bibliography 248
Subject Index 260
Author Index 263
|
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| ctrlnum | (OCoLC)38073339 (DE-599)BVBBV011951979 |
| dewey-full | 515/.243321 515/.2433 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:04Z |
| institution | BVB |
| isbn | 0387984534 |
| language | English |
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| physical | XIII, 265 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Wavelets, approximation and statistical applications Wolfgang Härdle ... New York [u.a.] Springer 1998 XIII, 265 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 129 Approximation, Théorie de l' Approximation, théorie de l' ram Benaderingen (wiskunde) gtt Non-parametrische statistiek gtt Ondelettes Ondelettes ram Schattingstheorie gtt Statistique non paramétrique Wavelets gtt Wavelets (Mathematics) Approximation theory Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Wavelet (DE-588)4215427-3 s Approximationstheorie (DE-588)4120913-8 s Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 Approximation (DE-588)4002498-2 s Härdle, Wolfgang 1953- Sonstige (DE-588)110357116 oth Lecture notes in statistics 129 (DE-604)BV002447846 129 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008080598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wavelets, approximation and statistical applications Lecture notes in statistics Approximation, Théorie de l' Approximation, théorie de l' ram Benaderingen (wiskunde) gtt Non-parametrische statistiek gtt Ondelettes Ondelettes ram Schattingstheorie gtt Statistique non paramétrique Wavelets gtt Wavelets (Mathematics) Approximation theory Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd Approximation (DE-588)4002498-2 gnd Wavelet (DE-588)4215427-3 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4002498-2 (DE-588)4215427-3 (DE-588)4120913-8 |
| title | Wavelets, approximation and statistical applications |
| title_auth | Wavelets, approximation and statistical applications |
| title_exact_search | Wavelets, approximation and statistical applications |
| title_full | Wavelets, approximation and statistical applications Wolfgang Härdle ... |
| title_fullStr | Wavelets, approximation and statistical applications Wolfgang Härdle ... |
| title_full_unstemmed | Wavelets, approximation and statistical applications Wolfgang Härdle ... |
| title_short | Wavelets, approximation and statistical applications |
| title_sort | wavelets approximation and statistical applications |
| topic | Approximation, Théorie de l' Approximation, théorie de l' ram Benaderingen (wiskunde) gtt Non-parametrische statistiek gtt Ondelettes Ondelettes ram Schattingstheorie gtt Statistique non paramétrique Wavelets gtt Wavelets (Mathematics) Approximation theory Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd Approximation (DE-588)4002498-2 gnd Wavelet (DE-588)4215427-3 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Approximation, Théorie de l' Approximation, théorie de l' Benaderingen (wiskunde) Non-parametrische statistiek Ondelettes Schattingstheorie Statistique non paramétrique Wavelets Wavelets (Mathematics) Approximation theory Nonparametric statistics Nichtparametrische Statistik Approximation Wavelet Approximationstheorie |
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