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

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    This study defines a sampling taxonomy to clarify the bootstrap, jackknife, and randomization test methods. This framework aids in understanding empirical sampling distributions for statistical analysis and hypothesis testing.

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    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.