Abstract

Clustered effects are often encountered in multiple hypothesis testing of spatial

signals. In this paper, we propose a new method, termed two-dimensional spatial multiple

testing (2d-SMT) procedure, to control the false discovery rate (FDR) and improve the detection power by exploiting the spatial information encoded in neighboring observations. The

proposed method provides a novel perspective of utilizing spatial information by gathering

signal patterns and spatial dependence into an auxiliary statistic. 2d-SMT rejects the null

when a primary statistic at the location of interest and the auxiliary statistic constructed

based on nearby observations are greater than their corresponding cutoffs. 2d-SMT can also

be combined with different variants of the weighted BH procedures to improve the detection

power further. A fast algorithm is developed to accelerate the search for optimal cutoffs in

2d-SMT. In theory, we establish the asymptotic FDR control of 2d-SMT under weak spatial

dependence. Extensive numerical experiments demonstrate that the 2d-SMT method combined with various weighted BH procedures achieves the most competitive performance in

FDR and power trade-off.

Information

Preprint No.SS-2024-0152
Manuscript IDSS-2024-0152
Complete AuthorsLinsui Deng, Kejun He, Xianyang Zhang
Corresponding AuthorsKejun He
Emailskejunhe@ruc.edu.cn

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Acknowledgments

The authors thank the editor, the associate editor, and anonymous reviewers for

their helpful comments and suggestions. This research was supported by the Public

Computing Cloud, Renmin University of China. The research of Zhang was partially

supported by NSF DMS-2113359, NIH 1R01GM144351-01 and NIH 1R21HG011662.

Supplementary Materials

The online Supplementary Material contains our proofs of Theorems 1 and 2, additional numerical results, some discussions about the estimation for the covariance

of noises, the details of Algorithm 1, and the address to download the reproducible

code of this work.

Supplementary materials are available for download.