  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.
