The Annals of Statistics

Robust functional principal components: A projection-pursuit approach

Juan Lucas Bali, Graciela Boente, David E. Tyler, and Jane-Ling Wang

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Abstract

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.

Article information

Source
Ann. Statist., Volume 39, Number 6 (2011), 2852-2882.

Dates
First available in Project Euclid: 24 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1327413771

Digital Object Identifier
doi:10.1214/11-AOS923

Mathematical Reviews number (MathSciNet)
MR3012394

Zentralblatt MATH identifier
1246.62145

Subjects
Primary: 62G35: Robustness 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62G20: Asymptotic properties

Keywords
Fisher-consistency functional data method of sieves penalization principal component analysis outliers robust estimation

Citation

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


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References

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Supplemental materials

  • 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.