Among inferential problems in functional data analysis, domain selection is one of the practical interests aiming to identify sub-interval(s) of the domain where desired functional features are displayed. Motivated by applications in quantitative ultrasound signal analysis, we propose the robust domain selection method, particularly aiming to discover a subset of the domain presenting distinct behaviors 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 behaviors among groups so that clinicians get a comprehensive understanding and select practically meaningful sub-interval(s). The performance of the proposed method is demonstrated through simulation studies and an application to motivating quantitative ultrasound measurements.

翻译：在泛函数据分析的推断问题中，域选择是旨在识别呈现所需泛函特征的子区间之一具有实际意义的问题。受定量超声信号分析应用的启发，我们提出鲁棒域选择方法，特别针对发现不同组间位置参数呈现不同行为的域子集。通过扩展区间检验方法，我们提出同时考虑泛函特征的多重方面以检测具有实际可解释性的域。为进一步处理收集的泛函轨迹中潜在的异常值和缺失片段，我们采用基于泛函M估计量的检验统计量进行区间检验推断。此外，我们通过计算从最低到最大尺度上鲁棒化效应量构建效应量热力图，以反映组间动态泛函行为，使临床医生能够全面理解并选择具有实际意义的子区间。通过模拟研究和激励性定量超声测量的应用验证了所提方法的性能。