The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 6 (2011), 2852-2882.
Robust functional principal components: A projection-pursuit approach
In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes.
Ann. Statist., Volume 39, Number 6 (2011), 2852-2882.
First available in Project Euclid: 24 January 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G35: Robustness 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62G20: Asymptotic properties
Bali, Juan Lucas; Boente, Graciela; Tyler, David E.; Wang, Jane-Ling. Robust functional principal components: A projection-pursuit approach. Ann. Statist. 39 (2011), no. 6, 2852--2882. doi:10.1214/11-AOS923. https://projecteuclid.org/euclid.aos/1327413771
- Supplementary material A: Robust functional principal components. In this Supplement, we give the proof of some of the results stated in Sections 4 and 6.
- Supplementary material B: Robust functional principal components. In this Supplement, we report the results obtained in the Monte Carlo study for the raw estimators and for the penalized ones when the smoothing parameters are fixed.