A1453
Title: Model-based statistical depth for multivariate sparse functional data
Authors: Yue Mu - St. Jude Children\'s Research Hospital (United States) [presenting]
Abstract: Functional depth provides a powerful tool for ordering and characterizing complex data, yet most existing methods are developed for univariate functional observations and assume dense sampling. The aim is to introduce a norm-based depth framework tailored for multivariate functional data, where each observation consists of multiple correlated trajectories. By leveraging a reproducing kernel Hilbert space norm, the proposed multivariate depth simultaneously accounts for both within-trajectory variation and cross-component structure, enabling a coherent ranking of multivariate samples. To address the challenges of real-world data, where functional observations are often recorded at irregular and sparse time points, the method is extended to the sparse setting. This allows the norm-based depth to be estimated from limited noisy measurements. Extensive simulation studies are conducted to evaluate the method against existing functional depths. The results demonstrate that the proposed approach not only captures centrality and outlyingness more effectively in multivariate settings, but also preserves reliable performance under sparse designs. Applications to ALS datasets further illustrate the practical utility of the method, showing its ability to detect clinically meaningful outliers and provide consistent characterization of disease trajectories across multiple biomarkers.
