On two sample inference for eigenspaces in functional data analysis with dependent errors

We consider functional data analysis for randomly perturbed repeated time series with a general dependence structure of the error process. Specifically, the question of testing for equality of subspaces spanned by a finite number of eigenfunctions is addressed. The asymptotic distribution of standardized residual processes based on projections of eigenfunctions is derived. A two-sample test based on the residual processes is proposed together with a nuisance parameter free bootstrap procedure. Simulations illustrate finite sample properties.