Outlier Detection in Functional Observations With Applications to Profile Monitoring

摘要

The presence of outliers has serious adverse effects on the modeling and forecasting of functional data. Therefore, outlier detection, aiming at identifying abnormal functional curves from a dataset, is quite important. This article proposes a new testing procedure based on functional principal component analysis. Under mild conditions, the null distribution of the test statistic is shown to be asymptotically pivotal with a well-known asymptotic distribution. Simulation results demonstrate good finite-sample performance of the asymptotic test and detection procedure. Finally, by illustrating the connection between profile monitoring in statistical process control and outlier detection in functional data, we apply the proposed approach to a real-data example from a manufacturing process and show that it performs quite well in detecting outlying profiles. Supplementary Material for this article is posted online on the journal web site.