Uniform central limit theorems:
In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tu...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2014
|
| Edition: | Second edition |
| Series: | Cambridge studies in advanced mathematics
142 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text |
| Physical Description: | 1 online resource (xii, 472 Seiten) |
| ISBN: | 9781139014830 |
| DOI: | 10.1017/CBO9781139014830 |
Staff View
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| 520 | |a In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text | ||
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Record in the Search Index
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| contents | Machine generated contents note: 1. Donsker's theorem and inequalities; 2. Gaussian processes; sample continuity; 3. Definition of Donsker classes; 4. Vapnik-Cervonenkis combinatorics; 5. Measurability; 6. Limit theorems for VC-type classes; 7. Metric entropy with bracketing; 8. Approximation of functions and sets; 9. Two samples and the bootstrap; 10. Uniform and universal limit theorems; 11. Classes too large to be Donsker; Appendix A. Differentiating under an integral sign; Appendix B. Multinomial distributions; Appendix C. Measures on nonseparable metric spaces; Appendix D. An extension of Lusin's theorem; Appendix E. Bochner and Pettis integrals; Appendix F. Non-existence of some linear forms; Appendix G. Separation of analytic sets; Appendix H. Young-Orlicz spaces; Appendix I. Versions of isonormal processes |
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| dewey-full | 519.2 |
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| discipline | Mathematik |
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| edition | Second edition |
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| id | DE-604.BV043940740 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781139014830 |
| language | English |
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| physical | 1 online resource (xii, 472 Seiten) |
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| publishDate | 2014 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Dudley, Richard M. 1938- Verfasser (DE-588)121010996 aut Uniform central limit theorems R.M. Dudley, Massachusetts Institute of Technology Second edition Cambridge Cambridge University Press 2014 1 online resource (xii, 472 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 142 Machine generated contents note: 1. Donsker's theorem and inequalities; 2. Gaussian processes; sample continuity; 3. Definition of Donsker classes; 4. Vapnik-Cervonenkis combinatorics; 5. Measurability; 6. Limit theorems for VC-type classes; 7. Metric entropy with bracketing; 8. Approximation of functions and sets; 9. Two samples and the bootstrap; 10. Uniform and universal limit theorems; 11. Classes too large to be Donsker; Appendix A. Differentiating under an integral sign; Appendix B. Multinomial distributions; Appendix C. Measures on nonseparable metric spaces; Appendix D. An extension of Lusin's theorem; Appendix E. Bochner and Pettis integrals; Appendix F. Non-existence of some linear forms; Appendix G. Separation of analytic sets; Appendix H. Young-Orlicz spaces; Appendix I. Versions of isonormal processes In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text 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 978-0-521-49884-5 Erscheint auch als Druck-Ausgabe 978-0-521-73841-5 Cambridge studies in advanced mathematics 142 (DE-604)BV044781283 142 https://doi.org/10.1017/CBO9781139014830 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dudley, Richard M. 1938- Uniform central limit theorems Cambridge studies in advanced mathematics Machine generated contents note: 1. Donsker's theorem and inequalities; 2. Gaussian processes; sample continuity; 3. Definition of Donsker classes; 4. Vapnik-Cervonenkis combinatorics; 5. Measurability; 6. Limit theorems for VC-type classes; 7. Metric entropy with bracketing; 8. Approximation of functions and sets; 9. Two samples and the bootstrap; 10. Uniform and universal limit theorems; 11. Classes too large to be Donsker; Appendix A. Differentiating under an integral sign; Appendix B. Multinomial distributions; Appendix C. Measures on nonseparable metric spaces; Appendix D. An extension of Lusin's theorem; Appendix E. Bochner and Pettis integrals; Appendix F. Non-existence of some linear forms; Appendix G. Separation of analytic sets; Appendix H. Young-Orlicz spaces; Appendix I. Versions of isonormal processes 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, Massachusetts Institute of Technology |
| title_fullStr | Uniform central limit theorems R.M. Dudley, Massachusetts Institute of Technology |
| title_full_unstemmed | Uniform central limit theorems R.M. Dudley, Massachusetts Institute of Technology |
| 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/CBO9781139014830 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT dudleyrichardm uniformcentrallimittheorems |