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Uniform Central Limit Theorems

2nd Edition


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: May 2014
  • availability: Available
  • format: Paperback
  • isbn: 9780521738415

£ 46.99

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About the Authors
  • 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
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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2014
    • format: Paperback
    • isbn: 9780521738415
    • length: 482 pages
    • dimensions: 228 x 152 x 26 mm
    • weight: 0.65kg
    • availability: Available
  • 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.

  • Author

    R. M. Dudley, Massachusetts Institute of Technology
    R. M. Dudley is a Professor of Mathematics at the Massachusetts Institute of Technology in Cambridge, Massachusetts.

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