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.

翻译：功能性主要组成部分分析(FCCA)在数据涉及非古属特征时可能无效,因此,我们打算开发一种一般FPCA方法,以适应此类非古属案例,建造了Kenall $\tau$的功能,该功能具有相同的机能,作为共变函数,具有相同的机能。Kendall $\tau$的特制功能使其对数据分布不那么敏感。我们进一步将其应用于对FPCA的估计,并研究相应的非古属一致性。此外,通过全面的模拟研究和对用可磨损加速计监测器收集的物理活动数据的应用,可以证明拟议方法的有效性。