Weak Convergence and Empirical Processes
With Applications to Statistics
Published on 24. December 2012
Book
Paperback/Softback
XVI, 510 pages
978-1-4757-2547-6 (ISBN)
Description
This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.
Reviews / Votes
"...succeeds and complements Billingsleys classic work and will become the standard source of study and reference for students and researchers...." The StatisticianMore details
Product info
Paperback
Series
Language
English
Place of publication
New York, NY
United States
Target group
Research
Illustrations
biography
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 28 mm
Weight
789 gr
ISBN-13
978-1-4757-2547-6 (9781475725476)
DOI
10.1007/978-1-4757-2545-2
Schweitzer Classification
Other editions
New editions
A. W. van der Vaart | Jon A. Wellner
Weak Convergence and Empirical Processes
With Applications to Statistics
Book
07/2023
2nd Edition
Springer
€149.79
Shipment within 15-20 days
Additional editions
Aad van der Vaart | Jon Wellner
Weak Convergence and Empirical Processes
With Applications to Statistics
E-Book
03/2013
Springer
€234.33
Available for download
A.W. van der vaart | Jon Wellner
Weak Convergence and Empirical Processes
With Applications to Statistics
Book
11/2000
1st Edition
Springer
€235.39
Article exhausted; check for reprint
Content
1.1. Introduction.- 1.2. Outer Integrals and Measurable Majorants.- 1.3. Weak Convergence.- 1.4. Product Spaces.- 1.5. Spaces of Bounded Functions.- 1.6. Spaces of Locally Bounded Functions.- 1.7. The Ball Sigma-Field and Measurability of Suprema.- 1.8. Hilbert Spaces.- 1.9. Convergence: Almost Surely and in Probability.- 1.10. Convergence: Weak, Almost Uniform, and in Probability.- 1.11. Refinements.- 1.12. Uniformity and Metrization.- 2.1. Introduction.- 2.2. Maximal Inequalities and Covering Numbers.- 2.3. Symmetrization and Measurability.- 2.4. Glivenko-Cantelli Theorems.- 2.5. Donsker Theorems.- 2.6. Uniform Entropy Numbers.- 2.7. Bracketing Numbers.- 2.8. Uniformity in the Underlying Distribution.- 2.9. Multiplier Central Limit Theorems.- 2.10. Permanence of the Donsker Property.- 2.11. The Central Limit Theorem for Processes.- 2.12. Partial-Sum Processes.- 2.13. Other Donsker Classes.- 2.14. Tail Bounds.- 3.1. Introduction.- 3.2. M-Estimators.- 3.3. Z-Estimators.- 3.4. Rates of Convergence.- 3.5. Random Sample Size, Poissonization and Kac Processes.- 3.6. The Bootstrap.- 3.7. The Two-Sample Problem.- 3.8. Independence Empirical Processes.- 3.9. The Delta-Method.- 3.10. Contiguity.- 3.11. Convolution and Minimax Theorems.- A. Appendix.- A.1. Inequalities.- A.2. Gaussian Processes.- A.2.1. Inequalities and Gaussian Comparison.- A.2.2. Exponential Bounds.- A.2.3. Majorizing Measures.- A.2.4. Further Results.- A.3. Rademacher Processes.- A.4. Isoperimetric Inequalities for Product Measures.- A.5. Some Limit Theorems.- A.6. More Inequalities.- A.6.1. Binomial Random Variables.- A.6.2. Multinomial Random Vectors.- A.6.3. Rademacher Sums.- Notes.- References.- Author Index.- List of Symbols.