Multiple testing. Part I. Single-step procedures for control of general type I error rates.

Area of Science:

• Statistical Methodology
• Multiple Hypothesis Testing
• Computational Statistics

Background:

• Controlling Type I error rates is crucial in multiple hypothesis testing to avoid false positives.
• Existing methods often rely on specific assumptions about data distribution or subset pivotality.
• There is a need for flexible procedures that control generalized error rates under broad conditions.

Purpose of the Study:

• To propose general single-step multiple testing procedures for controlling arbitrary Type I error rate parameters.
• To introduce a novel approach utilizing the null distribution of test statistics rather than the data generating distribution.
• To develop methods that offer asymptotic Type I error rate control without stringent distributional assumptions.

Main Methods:

• Development of single-step procedures based on the null distribution of test statistics to derive cut-offs and adjusted p-values.
• Identification of an asymptotic domination condition for null distributions ensuring Type I error rate control.
• Proposal of an explicit null distribution based on the asymptotic distribution of scaled and shifted test statistics.
• Utilization of a general bootstrap algorithm for obtaining consistent estimators of the null distribution.

Main Results:

• The proposed procedures asymptotically control Type I error rates for general null hypotheses and arbitrary data generating distributions.
• In the context of family-wise error rate (FWER) control, the method yields single-step minP and maxT procedures.
• Single-step procedures employing consistent null distribution estimators demonstrate asymptotic Type I error rate control.
• The approach is validated through simulation studies and applied to genomic data.

Conclusions:

• The proposed single-step multiple testing framework offers a flexible and robust approach to error rate control.
• The use of test statistics' null distribution provides a powerful alternative to traditional methods.
• The bootstrap algorithm facilitates practical implementation of these advanced statistical procedures.