The Bootstrap, the Jackknife, and the Randomization Test: A Sampling Taxonomy

Area of Science:

• Statistics
• Computational Statistics

Background:

• Resampling methods like bootstrap, jackknife, and randomization tests are crucial in statistical analysis.
• Understanding the distinctions and relationships among these methods is essential for appropriate application.

Purpose of the Study:

• To define a simple sampling taxonomy that elucidates the differences and relationships among bootstrap, jackknife, and randomization tests.
• To provide a pedagogical tool for teaching the goals and purposes of resampling schemes.
• To identify potential new resampling approaches through taxonomic extension.

Main Methods:

• Development of a conceptual taxonomy based on sampling approaches (with/without replacement) and sample size manipulation (whole sample vs. subset).
• Application of the taxonomy to explain the core principles of bootstrap, jackknife, and randomization tests.
• Presentation of univariate and multivariate examples to illustrate the taxonomy's utility.

Main Results:

• A clear taxonomy is presented, differentiating resampling methods based on sampling strategy and sample size.
• The taxonomy highlights how each method aims to create empirical sampling distributions for statistical inference.
• The framework suggests potential for novel resampling techniques.

Conclusions:

• The defined taxonomy effectively clarifies the relationships and distinctions between major resampling methods.
• This framework serves as a valuable educational resource for statistical resampling.
• The taxonomy's extension opens avenues for exploring new statistical computational methods.