Projection-Based Outlier Detection in Interval-Valued Functional Data

2026-08-02

AI Summary

This study addresses the lack of robust anomaly detection methods for interval-valued functional data (IVFD) by proposing the first projection-based robust anomaly detection framework. The approach decomposes interval-valued functions into center and log-radius components, derives a joint low-dimensional representation via interval-valued functional principal component analysis (IFPCA), and introduces the Interval-valued Least Trimmed Function Score (ILTFS) to identify a robust reference subset. Anomaly decisions are made by computing empirical p-values based on projection distances and controlling the false discovery rate (FDR) using the Benjamini–Hochberg procedure. Theoretically, the finite-sample breakdown point of ILTFS is established, and algorithmically, a concentration step iteration with descent properties is developed. Experiments demonstrate that the proposed ILTFS-FDR method achieves superior detection performance and robustness on both simulated and high-frequency ETF datasets.

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.

Problem

• outlier detection
• interval-valued functional data
• robustness
• functional data analysis
• false discovery rate

Innovation

• interval-valued functional data
• projection-based outlier detection
• functional principal component analysis
• least trimmed scores
• false discovery rate