Exact testing with random permutations.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Permutation tests are widely used but often rely on a limited number of random permutations.
• Theoretical analyses typically assume the entire permutation group, leading to random permutation methods being viewed as approximations.
• There is a scarcity of literature on the exactness of random permutation testing.

Purpose of the Study:

• To provide a rigorous proof of exactness for random permutation tests.
• To offer an alternative perspective by framing the test as a conditional Monte Carlo test.
• To extend existing results and demonstrate their applicability to multiple testing procedures.

Main Methods:

• Conditional Monte Carlo testing framework.
• Mathematical proof of exactness for random permutations.
• Extension of theoretical results.

Main Results:

• Demonstration that random permutation tests can achieve exactness.
• Validation of the conditional Monte Carlo approach for permutation testing.
• Theoretical groundwork for analyzing multiple testing procedures.

Conclusions:

• Random permutation tests are not inherently approximate and can be exact.
• The conditional Monte Carlo framework provides a robust method for proving exactness.
• These findings have significant implications for the theoretical underpinnings of multiple testing procedures.