Cooks distance measures for varying coefficient models with functional responses

The aim of this article is to develop Cooks distance measures for assessing the influence of both atypical curves and observations under varying coefficient model with functional responses. Our Cooks distance measures include Cooks distances for deleting multiple curves and for deleting multiple grid points, and their scaled Cooks distances. We systematically investigate some theoretical properties of these diagnostic measures. Simulation studies are conducted to evaluate the finite sample properties of these Cooks distances under different scenarios. A real diffusion tensor tract dataset is analyzed to illustrate the use of our diagnostic measures.