Uniform central limit theorems:
This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including seve...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
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| Schriftenreihe: | Cambridge studies in advanced mathematics
63 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 436 Seiten) |
| ISBN: | 9780511665622 |
| DOI: | 10.1017/CBO9780511665622 |
Internformat
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems | |
| 520 | |a This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory | ||
| 650 | 4 | |a Central limit theorem | |
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Datensatz im Suchindex
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| author | Dudley, Richard M. 1938- |
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| author_sort | Dudley, Richard M. 1938- |
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| bvnumber | BV043942384 |
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| contents | 1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems |
| ctrlnum | (ZDB-20-CBO)CR9780511665622 (OCoLC)992883868 (DE-599)BVBBV043942384 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511665622 |
| format | Electronic eBook |
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| id | DE-604.BV043942384 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511665622 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351354 |
| oclc_num | 992883868 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 online resource (xiv, 436 Seiten) |
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| publishDate | 1999 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Dudley, Richard M. 1938- Verfasser (DE-588)121010996 aut Uniform central limit theorems R.M. Dudley Cambridge Cambridge University Press 1999 1 online resource (xiv, 436 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 63 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd rswk-swf Zentraler Grenzwertsatz (DE-588)4067618-3 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-46102-3 Erscheint auch als Druck-Ausgabe 978-0-521-05221-4 https://doi.org/10.1017/CBO9780511665622 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dudley, Richard M. 1938- Uniform central limit theorems 1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| subject_GND | (DE-588)4067618-3 |
| title | Uniform central limit theorems |
| title_auth | Uniform central limit theorems |
| title_exact_search | Uniform central limit theorems |
| title_full | Uniform central limit theorems R.M. Dudley |
| title_fullStr | Uniform central limit theorems R.M. Dudley |
| title_full_unstemmed | Uniform central limit theorems R.M. Dudley |
| title_short | Uniform central limit theorems |
| title_sort | uniform central limit theorems |
| topic | Central limit theorem Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| topic_facet | Central limit theorem Zentraler Grenzwertsatz |
| url | https://doi.org/10.1017/CBO9780511665622 |
| work_keys_str_mv | AT dudleyrichardm uniformcentrallimittheorems |