Functional response regression analysis

In this paper, we study functional regression with a random response curve and vector covariates. We propose a supervised least squares estimation procedure after utilizing B-spline functions to approximate the unknown functions and establish the asymptotic normality of the proposed estimators. The method has an analytic form and is easily implemented. Compared to existing methods, it does not rely on a normality assumption and can be broadly applied to sparse or non-sparse, equally or non-equally spaced, and balanced or unbalanced observations. We assess the numerical performance of the proposed procedure through simulation experiments and illustrate its performance on a real example.