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Abstract:
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Nonlinear regression methods for Functional Data Analysis, FDA have received a fair amount of attention for the scalar-on-function case. Fully functional regression models, where the relationship between the response and covariates is believed to be nonlinear, have received less attention in the literature. Despite the lack of research on nonlinear regression with scalar-on-function models and nonlinear function-function models, many scholars have laid the ground work for developing these models. In this work, we develop a nonlinear function-on-function model using Reproducing Kernel Hilbert Spaces, RKHS for real-valued functions. We establish the minimax rate of convergence of the excess prediction risk. Our simulation studies faced computational challenges due to the complexity of the estimation procedure. We examine the prediction performance accuracy of our model through a simulation study. Our nonlinear function-function model is applied to Cumulative intraday return (CIDR) data in order to investigate the prediction performance of Standard & Poor's 500 Index (S&P 500) and the Dow Jones Industrial Average (DJIA) for General Electric Company (GE) and International Business Machines Corp.(IBM) for the three periods defining the crisis: ``Before," `` During," and `` After''.
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