Author | Vaart, Aad W. van der. author |
---|---|
Title | Weak Convergence and Empirical Processes [electronic resource] : With Applications to Statistics / by Aad W. van der Vaart, Jon A. Wellner |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-2545-2 |
Descript | XVI, 510 p. online resource |
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