Testing and Support Recovery in Population-Based Image Data
提出一种多尺度自适应检验方法，用于检测高维平滑图像数据中两组样本的差异，能识别差异位置，并扩展到多样本方差分析，在阿尔茨海默病数据中表现优于非多尺度方法。
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.