Name: Weak Convergence and Empirical Processes By Aad van der Vaart
SKU: 9781475725476
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Weak Convergence and Empirical Processes Summary

Weak Convergence and Empirical Processes: With Applications to Statistics by Aad van der Vaart

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.

Weak Convergence and Empirical Processes Reviews

...succeeds and complements Billingsleys classic work and will become the standard source of study and reference for students and researchers.... The Statistician

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.

Additional information

Sku

NLS9781475725476

ISBN 13

9781475725476

ISBN 10

1475725477

Title

Weak Convergence and Empirical Processes: With Applications to Statistics by Aad van der Vaart

Author

Aad van der Vaart

Series

Springer Series in Statistics

Condition

New

Binding type

Paperback

Publisher

Springer-Verlag New York Inc.

Year published

2012-12-24

Number of pages

510

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Weak Convergence and Empirical Processes Aad van der Vaart

Weak Convergence and Empirical Processes by Aad van der Vaart

Summary

Weak Convergence and Empirical Processes Summary

Weak Convergence and Empirical Processes: With Applications to Statistics by Aad van der Vaart

Weak Convergence and Empirical Processes Reviews

Table of Contents

Additional information

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