Testing and Support Recovery in Population-Based Image Data

In this article, we propose a multiscale adaptive test to detect differences between two samples of intrinsically smoothed image data in high-dimensional context. The test aggregates data from nearby locations using adaptive weights, significantly enhancing statistical power. We demonstrate that the test statistic converges to a Gumbel extreme value distribution under the null hypothesis. Moreover, we investigate its multiscale nature, showing that the chosen scales can grow at a specific polynomial rate of the sample size. We also evaluate its power against sparse alternatives and establish that with probability approaching one, the proposed method can identify the locations where the two means differ from each other. Additionally, we extend the proposed method to multi-sample ANOVA tests. Simulation results suggest that the proposed test outperforms the non-multiscale method that ignores spatial features of imaging data. The procedures are illustrated using a real dataset from the Alzheimer’s Disease Neuroimaging Initiative study. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.