Robust functional principal components: A projection-pursuit approach

TL;DR

This paper introduces a robust projection-pursuit method for functional principal component analysis, combining smoothing techniques to improve robustness and consistency in the presence of contaminated data.

Contribution

It adapts the projection pursuit approach to functional data, providing a robust estimation framework with proven consistency and improved performance over classical methods.

Findings

Robust estimators outperform classical ones under contamination.

The proposed method shows consistent estimation in simulations.

Performance depends on the smoothing technique used.

Abstract

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes.