区间值函数数据中基于投影的异常值检测
Projection-Based Outlier Detection in Interval-Valued Functional Data
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中文总结 AI 辅助
针对区间值函数数据的异常值检测需求，提出ILTFS-FDR方法，结合IFPCA与ILTFS，经模拟和高频ETF数据验证，可有效检测异常观测，兼具鲁棒性。
中文摘要 AI 辅助
异常值检测是确保统计建模和推断可靠的基础任务。区间值函数数据（IVFD）中每个观测由区间值曲线表示，可保留观测内部的变异性与不确定性，在统计学及相关应用中受关注度日益提升。因此，为IVFD开发有效的异常值检测方法是重要的方法论问题。为解决该问题，我们提出了一种鲁棒的基于投影的异常值检测框架：首先通过中心函数和对数半径函数表示每个区间值函数观测，应用区间值函数主成分分析（IFPCA）得到联合低维表示；接着引入区间值最小修剪函数得分（ILTFS）方法，通过最小化标准化IFPCA得分距离的修剪聚合项识别鲁棒参考子集；最后，我们提出ILTFS-FDR异常值检测方法，将所得投影距离转换为经验p值，并使用Benjamini–Hochberg程序在预先指定的目标错误发现率水平下进行调整。理论上，我们推导了ILTFS均值估计量的有限样本崩溃点，建立了浓度步算法的下降性质。模拟研究和对高频ETF数据的实证应用表明，所提出的ILTFS-FDR方法在检测异常区间值函数观测时具有有效性和鲁棒性。
英文摘要
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.
