Robust Functional Principal Component Analysis for Non-Gaussian Continuous Data to Analyze Physical Activity Data Generated by Accelerometers

Motivated by energy expenditure observations measured by wearable device, we propose two functional principal component analysis (FPCA) methods, Spearman FPCA and Kendall FPCA, for non-Gaussian continuous data. The energy expenditure records measured during physical activity can be modeled as functional data. They often involve non-Gaussian features, where the classical FPCA could be invalid. To handle this issue, we develop two robust FPCA estimators using the framework of rank statistics. Via an extension of the Spearman's rank correlation estimator and the Kendall's $\tau$ correlation estimator, a robust algorithm for FPCA is developed to fit the model. The two estimators are applied to analyze the physical activity data collected by a wearable accelerometer monitor. The effectiveness of the proposed methods is also demonstrated through a comprehensive simulation study.