  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.
