Robust smoothed canonical correlation analysis for functional data

TL;DR

This paper introduces robust estimators for canonical correlation analysis of functional data, ensuring consistency and reliability in the presence of data contamination or outliers.

Contribution

It develops robust estimation methods for functional canonical correlation analysis using association measures, basis expansion, and penalization, with proven consistency.

Findings

Estimators are consistent under regularity conditions.

Robust methods outperform traditional ones in contaminated data scenarios.

The approach integrates basis expansion and penalization for regularization.

Abstract

This paper provides robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by using robust association and scale measures combined with basis expansion and/or penalizations as a regularization tool. Under regularity conditions, the resulting estimators are consistent.