Journal
BIOMETRIKA
Volume 104, Issue 2, Pages 411-423Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asx012
Keywords
Functional principal component analysis; Least-trimmed-squares estimator; Masking; Reweighting; Robustness; Swamping
Funding
- National Natural Science Foundation of China and Singapore AcRF Tier 1 funding
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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.
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