Inverse problems and high-dimensional estimation: stats in the Château summer school, August 31 - September 4, 2009
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berling [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in statistics
203 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 198 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642199887 9783642199882 |
Internformat
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| 245 | 1 | 0 | |a Inverse problems and high-dimensional estimation |b stats in the Château summer school, August 31 - September 4, 2009 |c Pierre Alquier ... ed. |
| 264 | 1 | |a Berling [u.a.] |b Springer |c 2011 | |
| 300 | |a XIII, 198 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in statistics |v 203 | |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
PART I LECTURE NOTES ON INVERSE PROBLEMS 1 INVERSE PROBLEMS IN
STATISTICS 3
LAURENT CAVALIER 1.1 INVERSE PROBLEMS 4
1.1 INTRODUCTION 4
1.2 STATISTICAL INVERSE PROBLEMS 6
1.3 LINEAR INVERSE PROBLEMS WITH RANDOM NOISE 7 1.4 BASIC NOTIONS ON
OPERATOR THEORY 9
1.5 SINGULAR VALUE DECOMPOSITION AND SEQUENCE SPACE MODEL 13
1.1.6 EXAMPLES 16
1.1.7 SPECTRAL THEORY 23
1.2 NONPARAMETRIC ESTIMATION 27
1.2.1 MINIMAX APPROACH 28
1.2.2 REGULARIZATION METHODS 29
1.2.3 CLASSES OF FUNCTIONS 38
1.2.4 RATES OF CONVERGENCE 42
1.2.5 COMPARISON BETWEEN DETERMINISTIC AND STOCHASTIC NOISE 48 1.3
ADAPTATION AND ORACLE INEQUALITIES 53
1.3.1 MINIMAX ADAPTIVE PROCEDURES 53
1.3.2 ORACLE INEQUALITIES 55
1.3.3 MODEL SELECTION 57
1.3.4 UNIVERSAL OPTIMALITY 75
1.4 CONCLUSION 84
1.4.1 SUMMARY 84
1.4.2 DISCUSSION 86
1.4.3 OPEN PROBLEMS 87
REFERENCES 92
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010287451
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
PART II INVITED CONTRIBUTION ON INVERSE PROBLEMS
2 NON-PARAMETRIC MODELS WITH INSTRUMENTAL VARIABLES 99 JEAN-PIERRE
FLORENS 2.1 INTRODUCTION 99
2.2 THE LINEAR MODEL: VECTORIAL OR FUNCTIONAL DATA 102
2.3 THE ADDITIVELY SEPARABLE MODEL AND ITS EXTENSIONS 106 2.4 THE
NON-SEPARABLE MODELS I LL
2.5 SOME EXTENSIONS TO DYNAMIC MODELS 113
2.6 CONCLUSION 115
REFERENCES 116
PART III LECTURE NOTES ON HIGH-DIMENSIONAL ESTIMATION
3 HIGH DIMENSIONAL SPARSE ECONOMETRIC MODELS: AN INTRODUCTION . 121
ALEXANDRE BELLONI AND VICTOR CHERNOZHUKOV 3.1 THE HIGH DIMENSIONAL
SPARSE ECONOMETRIC MODEL 121 3.2 THE SETTING AND ESTIMATORS 127
3.2.1 THE MODEL 127
3.2.2 LASSO AND POST-LASSO ESTIMATORS 129
3.2.3 INTUITION AND GEOMETRY OF LASSO AND POST-LASSO . . . 131 3.2.4
PRIMITIVE CONDITIONS 133
3.3 ANALYSIS OF LASSO 135
3.4 MODEL SELECTION PROPERTIES AND SPARSITY OF LASSO 137 3.4.1 SPARSITY
BOUNDS 137
3.4.2 PERFECT MODEL SELECTION RESULTS 138
3.5 ANALYSIS OF POST-LASSO 139
3.6 ESTIMATION OF NOISE LEVEL 141
3.7 MONTE CARLO EXPERIMENTS 142
3.8 APPLICATION TO CROSS-COUNTRY GROWTH REGRESSION 146 APPENDIX 147
3.9 PROOFS 147
3.10 AUXILIARY LEMMAS 153
REFERENCES 155
PART IV INVITED CONTRIBUTIONS ON HIGH-DIMENSIONAL ESTIMATION
4 MODEL SELECTION IN GAUSSIAN REGRESSION FOR HIGH-DIMENSIONAL DATA . 159
FELIX ABRAMOVICH AND VADIM GRINSHTEIN 4.1 INTRODUCTION 159
4.2 PREAMBLE 161
4.3 NEARLY-ORTHOGONAL DESIGN 163
4.4 MULTICOLLINEAR DESIGN 165
4.5 BAYESIAN PERSPECTIVE 166
4.6 CONCLUDING REMARKS 168
REFERENCES 169
IMAGE 3
CONTENTS XI
5 BAYESIAN PERSPECTIVES ON SPARSE EMPIRICAL BAYES ANALYSIS (SEBA) . 171
NATALIA BOCHKINA AND YA'ACOV RITOV 5.1 INTRODUCTION 171
5.2 THE LASSOES PROCEDURE 174
5.2.1 PERSISTENCY AND BAYESIAN INTERPRETATION 174
5.2.2 RESTRICTED EIGENVALUES CONDITION AND ORACLE INEQUALITIES 177 5.3
GROUP LASSO: BAYESIAN PERSPECTIVE 180
5.4 RING LASSO: BAYESIAN PERSPECTIVE 182
REFERENCES 189
PART V INVITED AND CONTRIBUTED TALKS GIVEN DURING THE SUMMER SCHOOL
A LIST OF THE COURSES 193
B LIST OF THE INVITED TALKS 195
C LIST OF THE CONTRIBUTED TALKS AND POSTERS 197 |
| any_adam_object | 1 |
| author2 | Alquier, Pierre |
| author2_role | edt |
| author2_variant | p a pa |
| author_facet | Alquier, Pierre |
| building | Verbundindex |
| bvnumber | BV039140085 |
| classification_rvk | SI 856 SK 840 SK 920 |
| ctrlnum | (OCoLC)724965262 (DE-599)DNB1010287451 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV039140085 |
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| indexdate | 2024-07-20T11:14:44Z |
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| isbn | 3642199887 9783642199882 |
| language | English |
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| physical | XIII, 198 S. Ill., graph. Darst. 235 mm x 155 mm |
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| publisher | Springer |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 Pierre Alquier ... ed. Berling [u.a.] Springer 2011 XIII, 198 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 203 Literaturangaben Inverses Problem (DE-588)4125161-1 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Lasso-Methode (DE-588)7750854-3 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2009 Jouy-en-Josas gnd-content Statistik (DE-588)4056995-0 s Inverses Problem (DE-588)4125161-1 s DE-604 Regressionsmodell (DE-588)4127980-3 s Schätzung (DE-588)4193791-0 s Lasso-Methode (DE-588)7750854-3 s Bayes-Verfahren (DE-588)4204326-8 s Alquier, Pierre edt Erscheint auch als Online-Ausgabe 978-3-642-19989-9 Lecture notes in statistics 203 (DE-604)BV002447846 203 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3677702&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024158152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 Lecture notes in statistics Inverses Problem (DE-588)4125161-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Schätzung (DE-588)4193791-0 gnd Lasso-Methode (DE-588)7750854-3 gnd Regressionsmodell (DE-588)4127980-3 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4204326-8 (DE-588)4193791-0 (DE-588)7750854-3 (DE-588)4127980-3 (DE-588)4056995-0 (DE-588)1071861417 |
| title | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 |
| title_auth | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 |
| title_exact_search | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 |
| title_full | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 Pierre Alquier ... ed. |
| title_fullStr | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 Pierre Alquier ... ed. |
| title_full_unstemmed | Inverse problems and high-dimensional estimation stats in the Château summer school, August 31 - September 4, 2009 Pierre Alquier ... ed. |
| title_short | Inverse problems and high-dimensional estimation |
| title_sort | inverse problems and high dimensional estimation stats in the chateau summer school august 31 september 4 2009 |
| title_sub | stats in the Château summer school, August 31 - September 4, 2009 |
| topic | Inverses Problem (DE-588)4125161-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Schätzung (DE-588)4193791-0 gnd Lasso-Methode (DE-588)7750854-3 gnd Regressionsmodell (DE-588)4127980-3 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Inverses Problem Bayes-Verfahren Schätzung Lasso-Methode Regressionsmodell Statistik Konferenzschrift 2009 Jouy-en-Josas |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3677702&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024158152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
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