Local perturbation analysis of functional regression with applications

For a special functional regression model, i.e., both the dependent and independent variables are functions, we propose the concept of continuous-time perturbation analysis. For three perturbation schemes which correspond to the independent variable, dependent variable and weight function respectively,we obtain the closed form of the diagnosis function based on the functional optimization theory.As an application, we applied this approach to the system of ordinary differential equations (ODEs) and discovered the so-called boundary effect of two-step estimation ofODEs which leaves the possibility for future improvement of two-step estimation.