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Robust functional principal components by least trimmed squares Van Aelst, Stefan


Classical functional principal component analysis can yield erroneous approximations in pres- ence of outliers. To reduce the influence of atypical data we propose two methods based on trimming: a multivariate least trimmed squares (LTS) estimator and a componentwise variant. The multivariate LTS minimizes the least squares criterion over subsets of curves. The componentwise version minimizes the sum of univariate LTS scale estimators in each of the components. In general the curves can be considered as realizations of a random element on a separable Hilbert space. For a fixed dimension q, we then aim to robustly estimate the q-dimensional linear subspace that gives the best approximation to the functional data. Following Boente and Salibin-Barrera (2014) our estimators uses smoothing to first represent irregu- larly spaced curves in a high-dimensional space and then calculates the LTS solution on these multivariate data. The solution of the multivariate data is subsequently mapped back onto the Hilbert space. Poorly fitted observations can then be flagged as outliers. A simulation study and real data applications show that our estimators yield competitive results, both in identifying outliers and approximating regular data when compared to other existing methods.

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