Functional outlier detection with robust functional principal component analysis

• Published in: Computational statistics Vol. 27; no. 1; pp. 83 - 102
• Main Authors: Sawant, Pallavi, Billor, Nedret, Shin, Hyejin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.03.2012; Springer Nature B.V
• Subjects: Chemometrics; Combinatorics; Computation; Computer simulation; Covariance; Data analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematical analysis; Mathematical models; Mathematics and Statistics; Methods; Original Paper; Principal component analysis; Principal components analysis; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Studies; Outliers; Robust methods; Functional data; Principal component analysis
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-011-0239-3

Functional principal component analysis is the preliminary step to represent the data in a lower dimensional space and to capture the main modes of variability of the data by means of small number of components which are linear combinations of original variables. Sensitivity of the variance and the covariance functions to irregular observations make this method vulnerable to outliers and may not capture the variation of the regular observations. In this study, we propose a robust functional principal component analysis to find the linear combinations of the original variables that contain most of the information, even if there are outliers and to flag functional outliers. We demonstrate the performance of the proposed method on an extensive simulation study and two datasets from chemometrics and environment.