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Weak Convergence and Empirical Processes
Outer Integrals and Measurable Majorants
other
Author(s):
Aad W. van der Vaart
,
Jon A. Wellner
Publication date
(Print):
1996
Publisher:
Springer New York
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Book Chapter
Publication date (Print):
1996
Pages
: 6-15
DOI:
10.1007/978-1-4757-2545-2_2
SO-VID:
d716cb9b-0054-444b-953e-2c918448ad43
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Book chapters
pp. 2
Introduction
pp. 6
Outer Integrals and Measurable Majorants
pp. 16
Weak Convergence
pp. 29
Product Spaces
pp. 34
Spaces of Bounded Functions
pp. 43
Spaces of Locally Bounded Functions
pp. 45
The Ball Sigma-Field and Measurability of Suprema
pp. 49
Hilbert Spaces
pp. 52
Convergence: Almost Surely and in Probability
pp. 57
Convergence: Weak, Almost Uniform, and in Probability
pp. 67
Refinements
pp. 71
Uniformity and Metrization
pp. 80
Introduction
pp. 95
Maximal Inequalities and Covering Numbers
pp. 107
Symmetrization and Measurability
pp. 122
Glivenko-Cantelli Theorems
pp. 127
Donsker Theorems
pp. 134
Uniform Entropy Numbers
pp. 154
Bracketing Numbers
pp. 166
Uniformity in the Underlying Distribution
pp. 176
Multiplier Central Limit Theorems
pp. 190
Permanence of the Donsker Property
pp. 205
The Central Limit Theorem for Processes
pp. 225
Partial-Sum Processes
pp. 232
Other Donsker Classes
pp. 238
Tail Bounds
pp. 278
Introduction
pp. 284
M-Estimators
pp. 309
Z-Estimators
pp. 321
Rates of Convergence
pp. 339
Random Sample Size, Poissonization and Kac Processes
pp. 345
The Bootstrap
pp. 360
The Two-Sample Problem
pp. 367
Independence Empirical Processes
pp. 372
The Delta-Method
pp. 401
Contiguity
pp. 412
Convolution and Minimax Theorems
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