Robust domain selection for functional data via interval-wise testing and effect size mapping
提出一种稳健的域选择方法，通过区间检验和效应量热图识别函数型数据中不同组别位置参数差异显著的子区间，适用于定量超声信号分析等场景。
Abstract Among inferential problems in functional data analysis, domain selection is one of the practical interests aiming to identify subinterval(s) of the domain where desired functional features are displayed. Motivated by applications in quantitative ultrasound (QUS) signal analysis, we propose the robust domain selection method, particularly aiming to discover a subset of the domain presenting distinct behaviours on location parameters among different groups. By extending the interval testing approach, we propose to take into account multiple aspects of functional features simultaneously to detect the practically interpretable domain. To further handle potential outliers and missing segments on collected functional trajectories, we perform interval testing with a test statistic based on functional M-estimators for the inference. In addition, we introduce the effect size heatmap by calculating robustified effect sizes from the lowest to the largest scales over the domain to reflect dynamic functional behaviours among groups so that clinicians get a comprehensive understanding and select practically meaningful subinterval(s). The performance of the proposed method is demonstrated through simulation studies and an application to motivating QUS measurements.