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Room P3.10, Mathematics Building
Graciela Boente, Universidad de Buenos Aires and CONICET, Argentina
S-estimators for functional principal component analysis
A well-known property of functional principal components is that
they provide the best q-dimensional approximation to random
elements over separable Hilbert spaces. Our approach to robust
estimates of principal components for functional data is based on
this property since we consider the problem of robustly estimating
these finite-dimensional approximating linear spaces. We propose a
new class of estimators for principal components based on robust
scale functionals by finding the lower dimensional linear space
that provides the best prediction for the data. In analogy to the
linear regression case, we call this proposal S-estimators. This
method can also be applied to sparse data sets when the underlying
process satisfies a smoothness condition with respect to the
functional associated with the scale defining the S-estimators. The
motivation is a problem of outlier detection in atmospheric data
collected by weather balloons launched into the atmosphere and
stratosphere.