Projection-Based Outlier Detection in Interval-Valued Functional Data

Abstract

Outlier detection is a fundamental task for ensuring reliable statistical modeling and inference. Interval-valued functional data (IVFD), in which each observation is represented by an interval-valued curve that preserves the variability and uncertainty within the observation, have attracted increasing attention in statistics and related applications. Developing effective outlier detection procedures for IVFD is therefore an important methodological problem. To address this issue, we develop a robust projection-based outlier detection framework. We first represent each interval-valued functional observation through its center and log-radius functions and apply interval-valued functional principal component analysis (IFPCA) to obtain a joint low-dimensional representation. We then introduce the interval-valued least trimmed functional scores (ILTFS) method, which identifies a robust reference subset by minimizing a trimmed aggregate of standardized IFPCA score distances. Finally, we proposed the ILTFS-FDR outlier detection procedure by converting the resulting projection distances into empirical $p$-values and adjusting using the Benjamini--Hochberg procedure at a prespecified target false discovery rate level. Theoretically, we derive the finite-sample breakdown point of the ILTFS mean estimator and establish the descent property of the concentration-step algorithm. Simulation studies and an empirical application to high-frequency ETF data demonstrate the effectiveness and robustness of the proposed ILTFS-FDR procedure in detecting abnormal interval-valued functional observations.