  Functional principal component analysis is essential in functional data
analysis, but the inferences will become unconvincing when some non-Gaussian
characteristics occur, such as heavy tail and skewness. The focus of this paper
is to develop a robust functional principal component analysis methodology in
dealing with non-Gaussian longitudinal data, for which sparsity and
irregularity along with non-negligible measurement errors must be considered.
We introduce a Kendall's $\tau$ function whose particular properties make it a
nice proxy for the covariance function in the eigenequation when handling
non-Gaussian cases. Moreover, the estimation procedure is presented and the
asymptotic theory is also established. We further demonstrate the superiority
and robustness of our method through simulation studies and apply the method to
the longitudinal CD4 cell count data in an AIDS study.
