  We consider the problem of constructing confidence intervals for
nonparametric functional data analysis using empirical likelihood. In this
doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and
propose a bias-corrected construction that requires neither undersmoothing nor
direct bias estimation. We also extend our results to partially linear
regression involving functional data. Our numerical results demonstrated the
improved performance of empirical likelihood over approximation based on
asymptotic normality.
