Uniform Central Limit Theorems
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–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.
- A thoroughly revised second edition that includes updates and expansion of every chapter
- Includes a number of new proofs that were missing from the first edition
Product details
No date availablePaperback
9780521738415
482 pages
228 × 152 × 26 mm
0.65kg
Table of Contents
- 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.
