OUP accepted manuscript
提出一种基于高抗差均值函数估计的程序，通过函数主成分分析后的最小修剪平方投影系数识别异常值，并利用基于函数得分距离的渐近分布阈值控制误报率，有效检测函数型数据中的异常点。
We propose a procedure based on a high-breakdown mean function estimator to detect outliers in functional data. The robust estimator is obtained from a clean subset of observations, excluding potential outliers, by minimizing the least-trimmed-squares projection coefficients after functional principal component analysis. A threshold rule based on the asymptotic distribution of the functional score-based distance robustly controls the false positive rate and detects outliers effectively. Further improvement in power can be achieved by adding a one-step reweighting procedure. The finite-sample performance of our method demonstrates satisfactory false positive and false negative rates compared with existing outlier detection methods for functional data.