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Title: Regularized interaction models for function-on-function regression Authors:  Hidetoshi Matsui - Shiga University (Japan) [presenting]
Abstract: A regression model with a functional predictor and a functional response is considered. A functional quadratic model is an extension of a functional linear model and includes the quadratic term that takes the interaction between two different time points of the functional data into consideration. Predictor and the coefficient functions in the model are supposed to be expressed by basis expansions, and then parameters included in the model are estimated by the penalized likelihood method assuming that the error function follows a Gaussian process. Model selection criteria for evaluating the functional quadratic model are also derived using the idea of information-theoretic and Bayesian approach. The proposed method is applied to the analysis of meteorological data and the results are explored.