When Does Bootstrap Work?

Asymptotic Results and Simulations

0. Introduction.
1. Bootstrap and Asymptotic Normality.
1. Introduction.
2. Bootstrapping linear functionals. The i. i. d. case.
3. Bootstrapping smooth functionals.
4. Bootstrap and wild bootstrap in non i. i. d. models.
5. Some simulations.
6. Proofs.
Figures.
2. An Example Where Bootstrap Fails: Comparing Nonparametric Versus Parametric Regression Fits.
1. A goodness-of-fit test.
2. How to bootstrap. Bootstrap and wild bootstrap.
3. Proofs.
3. A Bootstrap Success Story: Using Nonparametric Density Estimates in K-Sample Problems.
1. Bootstrap tests.
2. Bootstrap confidence regions.
4. A Bootstrap Test on the Number of Modes of a Density.
2. The number of modes of a kernel density estimator.
3. Bootstrapping the test statistic.
4. Proofs.
5. Higher-Order Accuracy of Bootstrap for Smooth Functionals.
2. Bootstrapping smooth functionals.
3. Some more simulations. Bootstrapping an M-estimate.
4. Proof of the theorem.
6. Bootstrapping Linear Models.
1. Bootstrapping the least squares estimator.
2. Bootstrapping F-tests.
3. Proof of Theorem 3.
7. Bootstrapping Robust Regression.
2. Bootstrapping M-estimates.
3. Stochastic expansions of M-estimates.
8. Bootstrap and wild Bootstrap for High-Dimensional Linear Random Design Models.
2. Consistency of bootstrap for linear contrasts.
3. Accuracy of the bootstrap.
4. Bootstrapping F-tests.
5. Proofs.
Tables.
9. References.