Randomised P-values and nonparametric procedures in multiple testing.

Area of Science:

• Statistics
• Statistical Inference
• Hypothesis Testing

Background:

• Multiple hypothesis testing procedures for false discovery rate (FDR) control often assume P-value statistics are uniformly distributed under null hypotheses.
• This uniformity assumption can fail with discrete test statistics or misspecified distributional models for observables.

Purpose of the Study:

• To introduce a stochastic process framework that ensures P-value statistics satisfy the uniformity condition, even with discrete test statistics.
• To enhance the robustness of multiple testing procedures by allowing the use of nonparametric tests.

Main Methods:

• A stochastic process framework is developed utilizing a uniform variate.
• This framework enables P-value statistics to meet uniformity conditions irrespective of the test statistic's distribution.
• Nonparametric tests can be employed to generate P-value statistics that satisfy the uniformity condition.

Main Results:

• The proposed method ensures P-value statistics satisfy the uniformity condition, even when test statistics have discrete distributions.
• Multiple testing procedures using these P-values exhibit enhanced robustness properties.
• Simulation studies indicate improved performance of FDR methods with nonparametric randomized test P-values when the observable model is nonparametric or misspecified.

Conclusions:

• The introduced stochastic process framework provides a robust solution for multiple hypothesis testing under challenging distributional assumptions.
• Nonparametric randomized P-values enhance the reliability and performance of FDR control methods in complex statistical scenarios.
• This approach broadens the applicability of FDR control to a wider range of statistical models and data types.