Two-sample inference for sparse functional data

Abstract

In this paper, we develop an asymptotic ${\mathrm{\chi }}^2$ test for detecting differences among mean functions when sparse and irregular observations are drawn from the underlying continuous stochastic processes for each subject. We provide theoretical arguments to justify the effectiveness of the proposed test procedure. Numerical experiments, including simulation studies and applications to a CD4 count data set and an eBay online auction data set, are presented to demonstrate the good performance of the developed test.