M-type smoothing spline estimators for principal functions

Seokho Lee, Hyejin Shin and Nedret Billor

Computational Statistics & Data Analysis, 2013, vol. 66, issue C, 89-100

Abstract: We propose a robust method for estimating principal functions based on MM estimation. Specifically, we formulate functional principal component analysis into alternating penalized M-regression with a bounded loss function. The resulting principal functions are given as M-type smoothing spline estimators. Using the properties of a natural cubic spline, we develop a fast computation algorithm even for long and dense functional data. The proposed method is efficient in that the maximal information from whole observed curve is retained since it partly downweighs abnormally observed individual measurements in a single curve rather than removing or downweighing a whole curve. We demonstrate the performance of the proposed method on simulated and real data and compare it with the conventional functional principal component analysis and other robust functional principal component analysis techniques.

Keywords: Alternating regression; Rank-one approximation; Functional principal component analysis; MM estimation; Natural cubic splines (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:66:y:2013:i:c:p:89-100

DOI: 10.1016/j.csda.2013.03.022

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