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Uniform Central Limit Theorems 2nd Edition by RM Dudley ISBN 0521738415 9780521738415

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Uniform Central Limit Theorems 2ed. Edition Dudley R.M. Digital Instant Download

Author(s): Dudley R.M.
ISBN(s): 9780521738415, 0521738415
Edition: 2ed.
File Details: PDF, 3.26 MB
Year: 2014
Language: english
SKU: EB-4584034 Category: Tag:

Uniform Central Limit Theorems 2nd Edition by RM Dudley – Ebook PDF Instant Download/Delivery: 0521738415, 9780521738415
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Product details:

ISBN 10: 0521738415 
ISBN 13: 9780521738415
Author: RM Dudley

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.

Uniform Central Limit Theorems 2nd Table of contents:

1: Donsker’s Theorem, Metric Entropy, and Inequalities

1.1 Empirical Processes: The Classical Case
1.2 Metric Entropy and Capacity
1.3 Inequalities
1.4 Proof of the Bretagnolle­Massart Theorem
1.5 The DKW Inequality in Massart’s Form
Notes

2: Gaussian Processes; Sample Continuity

2.1 General Empirical and Gaussian Processes
2.2 Some Definitions
2.3 Bounds for Gaussian Vectors
2.4 Inequalities and Comparisons for Gaussian Distributions
2.5 Sample Boundedness
2.6 Gaussian Measures and Convexity
2.7 Sample Continuity
2.8 A Metric Entropy Condition Implying Sample Continuity
2.9 Gaussian Concentration Inequalities
2.10 Generic Chaining
2.11 Homogeneous and Quasi-homogeneous Sets in H
2.12 Sample Continuity and Compactness
2.13 Two-Series and One-Series Theorems
Notes

3: Foundations of Uniform Central Limit Theorems; Donsker Classes

3.1 Definitions: Convergence in Law
3.2 Measurable Cover Functions
3.3 Convergence Almost Uniformly and in Outer Probability
3.4 Perfect Functions
3.5 Almost Surely Convergent Realizations
3.6 Conditions Equivalent to Convergence in Law
3.7 Asymptotic Equicontinuity
3.8 Unions of Donsker Classes
3.9 Sequences of Sets and Functions
3.10 Closure of Donsker Classes under Sequential Limits
3.11 Convex Hulls of Donsker Classes
Notes

4: Vapnik–Červonenkis Combinatorics

4.1 Vapnik–Červonenkis Classes of Sets
4.2 Generating Vapnik–Červonenkis Classes
4.3 Maximal Classes
4.4 Classes of Index 1
4.5 Combining VC Classes
4.6 Probability Laws and Independence
4.7 Vapnik–Červonenkis Properties of Classes of Functions
4.8 Classes of Functions and Dual Density
Notes

5: Measurability

5.1 Sufficiency
5.2 Admissibility
5.3 Suslin Properties and Selection
Notes

6: Limit Theorems for Vapnik–Červonenkis and Related Classes

6.1 Koltchinskii–Pollard Entropy and Glivenko–Cantelli Theorems
6.2 Glivenko–Cantelli Properties for Given P
6.3 Pollard’s Central Limit Theorem
6.4 Necessary Conditions for Limit Theorems
Notes

7: Metric Entropy, with Inclusion and Bracketing

7.1 Definitions and the Blum–DeHardt Law of Large Numbers
7.2 Central Limit Theorems with Bracketing
7.3 The Power Set of a Countable Set: Borisov–Durst Theorem
Notes

8: Approximation of Functions and Sets

8.1 Introduction: The Hausdorff Metric
8.2 Spaces of Differentiable Functions and Sets with Differentiable Boundaries
8.3 Lower Layers
8.4 Metric Entropy of Classes of Convex Sets
Notes

9: The Two-Sample Case, the Bootstrap, and Confidence Sets

9.1 The Two-Sample Case
9.2 A Bootstrap Central Limit Theorem in Probability
9.3 Other Aspects of the Bootstrap
Notes

10: Uniform and Universal Limit Theorems

10.1 Uniform Glivenko-Cantelli Classes
10.2 Universal Donsker Classes
10.3 Metric Entropy of Convex Hulls in Hilbert Space
10.4 Uniform Donsker Classes
10.5 Universal Glivenko-Cantelli Classes
Problems
Notes

11: Classes of Sets or Functions Too Large for Central Limit Theorems

11.1 Universal Lower Bounds
11.2 An Upper Bound
11.3 Poissonization and Random Sets
11.4 Lower Bounds in Borderline Cases
11.5 Proof of Theorem 11.10

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Tags: RM Dudley, Uniform Central