Estimation and inference in partially functional linear regression with multiple functional covariates

In this paper, we consider the estimation and inference in partially functional linear regression with multiple functional covariates. We estimate the parameters and the slope functions by using functional principal component analysis (FPCA) approach to each functional covariate; establish the asymptotic distribution for the proposed estimators and investigate the semiparametric efficiency. We derive the rates of convergence for the estimators of the slope functions, and prove that the rates are optimal. We also develop a linear hypothesis test for the parametric component, and construct confidence bands centered at FPCA-based estimator for the slope functions and verify its asymptotic validity. The performance of the proposed procedures is illustrated via simulation studies and an analysis of a diffusion tensor imaging data application.