Robust domain selection for functional data via interval-wise testing and effect size mapping

TL;DR

This paper introduces a robust method for selecting meaningful sub-intervals in functional data, combining interval-wise testing with effect size mapping to improve interpretability and handle outliers, demonstrated through simulations and ultrasound data.

Contribution

It extends interval testing with functional M-estimators and effect size heatmaps for robust, interpretable domain selection in functional data analysis, especially in medical applications.

Findings

Effective in identifying relevant sub-intervals in simulated data.

Successfully applied to quantitative ultrasound measurements.

Robust to outliers and missing data.

Abstract

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.