Multivariate multiple test procedures based on nonparametric copula estimation.

Area of Science:

• Statistics
• Data Science
• Applied Mathematics

Background:

• Modern high-dimensional data often exhibits complex dependencies.
• Existing multiple testing procedures may not fully leverage these dependencies, potentially limiting statistical power.
• Copula functions offer a general framework for modeling dependency structures.

Purpose of the Study:

• To extend Bernstein copulae to the multivariate case for dependency modeling in multiple testing.
• To develop empirically calibrated confidence regions for the family-wise error rate (FWER).
• To assess the power gains achieved by exploiting dependencies compared to standard methods.

Main Methods:

• Utilizing Bernstein copulae for nonparametric estimation of multivariate dependency structures.
• Deriving asymptotic confidence regions for the FWER of multiple test procedures.
• Empirical calibration of tests using Bernstein copulae approximations.
• Simulation studies to compare performance against Bonferroni and Šidák corrections.

Main Results:

• Bernstein copulae effectively approximate multivariate dependency structures.
• The proposed method achieves better FWER level exhaustion, leading to increased statistical power.
• Demonstrated practical utility through an application to insurance data.

Conclusions:

• Exploiting data dependencies via multivariate Bernstein copulae significantly enhances the power of multiple testing procedures.
• The methodology offers a robust alternative to conventional corrections, particularly for high-dimensional data.
• The approach is applicable to real-world datasets, showing practical relevance.