Multiple Testing under Dependence via Semiparametric Graphical Models.

Area of Science:

• Statistics
• Statistical inference

Background:

• Graphical models enhance performance in large-scale multiple testing by leveraging data dependence.
• Current parametric graphical models require accurate knowledge of the alternative hypothesis density (f1), which is often difficult in practice.
• Heterogeneous f1 distributions cannot be estimated using simple parametric models.

Purpose of the Study:

• To propose a novel semiparametric approach for multiple testing under dependence.
• To develop a method that adaptively estimates the density function of the test statistic under the alternative hypothesis (f1).
• To generalize the local false discovery rate (fdr) procedure and connect with the Benjamini-Hochberg (BH) procedure.

Main Methods:

• A semiparametric approach is proposed to estimate f1 adaptively.
• The method generalizes the local false discovery rate (fdr) procedure.
• The approach connects with the Benjamini-Hochberg (BH) procedure.

Main Results:

• Simulations demonstrate that the semiparametric approach outperforms classical procedures that assume independence.
• The proposed method shows superior performance compared to parametric approaches that capture dependence.
• The adaptive estimation of f1 allows for more robust multiple testing.

Conclusions:

• The novel semiparametric approach offers improved performance for large-scale multiple testing problems with dependence.
• This method provides a flexible alternative to existing parametric and independence-assuming procedures.
• The adaptive estimation of f1 is key to the enhanced performance in complex scenarios.