Sequential Multiple Testing

2017/05/25 by Shiyun Chen, Chen, Shiyun, Ery Arias-Castro +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Biosensing Techniques and Applications #FOS: Mathematics #Gene expression and cancer classification #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1705.10190

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an online multiple testing problem where the hypotheses arrive sequentially in a stream. The test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We investigate two procedures LORD and LOND, proposed by (Javanmard and Montanari, 2015), which are proved to control the FDR in an online manner. In some (static) model, we show that LORD is optimal in some asymptotic sense, in particular as powerful as the (static) Benjamini-Hochberg procedure to first asymptotic order. We also quantify the performance of LOND. Some numerical experiments complement our theory.

Citations

• Sequential Tests of Multiple Hypotheses Controlling False Discovery and Nondiscovery Rates
• Optimal Inference After Model Selection
• On Online Control of False Discovery Rate
• Power of Ordered Hypothesis Testing

Related

• Sequential Tests of Multiple Hypotheses Controlling False Discovery and Nondiscovery Rates
• Asymptotically optimal sequential FDR and pFDR control with (or without) prior information on the number of signals
• Asymptotically Optimal Sequential Multiple Testing with Asynchronous Decisions
• Dynamic Algorithms for Online Multiple Testing
• An online generalization of the (e-)Benjamini-Hochberg procedure