Robust smoothed canonical correlation analysis for functional data

Abstract

This paper provides robust estimators for the first canonical correlation anddirections of random elements on Hilbert separable spaces by using robust association andscale measures combined with basis expansion and/or penalizations as a regularizationtool. Under regularity conditions, the resulting estimators are consistent. The finitesample performance of our proposal is illustrated through a simulation study that showsthat, as expected, the robust method outperforms the existing classical procedure whenthe data are contaminated. A real data example is also presented.