In classical statistics, confidence intervals and hypothesis tests rely on making distributional assumptions about the data generating process. Often, these assumptions are incorrect. The bootstrap and related techniques rely on resampling from the data to construct the required distributions, and thus they are guaranteed to be correct given sufficient data. These techniques don't work very well with a small number of data points, but they are extremely effective in the era of big data.
Recommended Books
An Introduction to the Bootstrap
Bradley Efron And Robert J. Tibshirani
Key Features
- In-text exercises
Key Topics
- Adaptive Estimation
- Approximate Likelihoods
- Bootstrap Confidence Intervals
- Bootstrap Estimate of Bias
- Bootstrap Estimate of Standard Error
- Bootstrap Hypothesis Testing
- Bootstrap for Regression Models
- Connections Between the Bootstrap and Classical Inference
- Cross Validation
- Efficient Bootstrap Computation
- Error in Bootstrap Estimates
- Geometry of the Bootstrap
- Parametric Bootstrap
- Permutation Tests
- Plug-In Principle
- Practical Considerations When Using the Bootstrap
- The Jackknife
Description
This is a great introduction to the bootstrap from its creator. It's quite gentle as statistical books go; the more challenging mathematics are relegated to the end of the book. Bootstrap hypothesis testing and confidence intervals receive excellent coverage, along with permutation testing, the jackknife, and other bootstrap-related topics. There is code that is written in the now largely defunct S language (the progenitor of R). It translates easily to R.