Two-sample functional linear models with functional responses

This paper studies two-sample functional linear regressions with functional responses, where the regression functions are assumed to have a scaling transformation. We estimate the intercept function, slope function, and parameter components based on the least squares method and functional principal component analysis. The proposed estimators of the parameter components are shown to be consistent and asymptotically normal. We also establish a rate of convergence for the estimator of the slope function. In addition, we propose asymptotically more efficient estimators for the parameter components. The numerical performance of the proposed methods is evaluated via simulation studies and an analysis of an AIDS data set.