A robust smoothed approach to functional canonical correlation analysis

BOENTE, GRACIELA; KUDRASZOW, NADIA

Viena

Conferencia; International Conference on Robust Statistics (ICORS 2021); 2021

Technische Universitat Wien

In this talk, we will focus on functional canonical correlation analysis, where data consist of pairs of random curves and the analysis tries to identify and quantify the relation between the observed functions. Under a Gaussian model, Leurgans, Moyeed, and Silverman (1993) showed that the natural extensionof multivariate estimators to the functional scenario fails, motivating the introduction ofregularization techniques which may combine smoothing through a penalty term and/orprojection of the observed curves on a nite{dimensional linear space generated by a givenbasis. The classical estimators use the Pearson correlation as measure ofthe association between the observed functions and for that reason they are sensitive tooutliers.To provide robust estimators for the first functional canonical correlation and directions,we will introduce two families of robust consistent estimators that combine robust associationand scale measures with basis expansion and/or penalizations as a regularizationtool. Both families turn out to be consistent under mild assumptions. We will present theresults of a numerical study that shows that, as expected, the robust method outperformsthe existing classical procedure when the data are contaminated A real data example willalso be presented.