A1628
Title: Function-on-function combined regression models
Authors: Shifan Jia - Simon Fraser University (Canada)
Haolun Shi - Simon Fraser University (Canada)
Tianyu Guan - York University (Canada) [presenting]
Abstract: A function-on-function combined regression model is proposed that predicts a functional response by both a nonlinear dynamic effect of a functional predictor and a linear concurrent effect of another functional predictor. The nonlinear dynamic effect is characterized by taking an integral of a time-dependent two-dimensional smooth surface, and the linear concurrent effect is modeled through a time-varying coefficient. The model structure combines the flexibility of nonlinear modeling with the interpretability of the linear concurrent effect. To approximate the two-dimensional surface, tensor product basis expansions are used, and for the time-varying coefficient in the concurrent effect, B-spline expansions are employed. The expansion parameters for each effect are estimated iteratively to account for the mutual dependencies between these two estimated effects. Each iteration of parameter estimation involves solving a penalized least squares problem. The asymptotic properties of the estimator are established. The numerical performance of the proposed method is illustrated by simulation studies and two real data applications.
