Functional principal component analysis estimator for non-Gaussian data

Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method that can adapt to such non-Gaussian cases. A Kendall's tau function, which possesses identical eigenfunctions as covariance function, is constructed. The particular formulation of Kendall's tau function makes it less sensitive 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 that collected by a wearable accelerometer monitor.