Functional principal component analysis estimator for non-Gaussian data

TL;DR

This paper introduces a novel FPCA method based on Kendall's tau function to effectively handle non-Gaussian functional data, ensuring more robust analysis.

Contribution

It develops a new FPCA estimator using Kendall's tau function that maintains eigenfunctions and improves robustness for non-Gaussian data.

Findings

The proposed method is asymptotically consistent.

Simulation studies demonstrate improved robustness.

Application to accelerometer data shows practical effectiveness.

Abstract

Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenall's $\tau$ function, which possesses identical eigenfunctions as covariance function, is constructed. The particular formulation of Kendall's $\tau$ function makes it less insensitive to data distribution. We further apply it to the estimation of FPCA and study the corresponding asymptotic consistency. Moreover, the effectiveness of the proposed method is demonstrated through a comprehensive simulation study and an application to the physical activity data collected by a wearable accelerometer monitor.