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Situation of resampling in
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Introduction to the Bootstrap
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Homeworks
Lectures
Subsections
Situation of resampling in contemporary statistics
Fisher's Classical Paradigm
Tukey and Mallow's Exploratory-Confirmatory Paradigm
The underlying principle
The questions addressed
The bootstrap: Some Examples
A binomial example
Computing the bootstrap distribution for one sample
Comparing to a hypothetical parameter
Computing the bootstrap distribution for two samples
Without the computer
First plug-in encounter
Some notation
Accuracy of the sample mean
Mouse example
The combinatorics of the bootstrap distribution
How many different bootstrap samples are there?
Which is the most likely bootstrap sample?
The
multinomial
distribution
Complete Enumeration
The original Gray code
Gray Codes for the Bootstrap
Gray codes for compositions.
Complete Bootstrap distribution for the Law School data
Balanced Bootstraps
Monte Carlo
What is a
Monte Carlo
Method?
Antithetic Resampling
Importance Sampling
More about the theoretical underpinnings of the Bootstrap
Statistical Functionals
Notions of Convergence
Why is the empirical cdf
a good estimator of F?
Generalized Statistical Functionals
Example and Counterexample
Bootstrap of the maximum
Theoretical Analysis
Parametric Bootstrap
Maximum
Correlation Coefficient
The jackknife
Example: Patch Data
Cross Validation
Cross-Validation when there is a response variable
Bootstrapping a Principal Component Analysis
Description of singular value Decomposition
Principal Components
Matlab for the Scores Example -in handout 4/27/99
How to generate a multivariate normal
Confidence Intervals
Studentized Confidence Intervals
Correlation Coefficient Example
Transformations of the parameter
The delta method
One dimension
The Smoothed Bootstrap
Smoothing- a crash course
Smoothing for variance stabilization
Susan Holmes 2004-05-19
a good estimator of F?