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

Robust functional principal components: a projection-pursuit approach. (English) Zbl 1246.62145

Ann. Stat. 39, No. 6, 2852-2882 (2011).
Summary: 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.

Cited in 1 Review
Cited in 35 Documents

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)

Keywords:

Fisher-consistency; functional data; method of sieves; penalization; outliers; robust estimation

Software:

fda (R); robustbase
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\textit{J. L. Bali} et al., Ann. Stat. 39, No. 6, 2852--2882 (2011; Zbl 1246.62145)
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