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Activity Number: 415 - Methods for Functional or Network Data
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #323620 View Presentation
Title: Interaction and Model Selection for Function-On-Function Regression
Author(s): Ruiyan Luo* and Xin Qi
Companies: Georgia State University and Georgia State University
Keywords: function-on-function regression ; interaction effects ; Karhunen-Loeve expansion ; model selection
Abstract:

Interaction terms are common in traditional regression models with scalar predictors and response. In functional regression, interactions have been considered in function-on-scalar or scalar-on-function regression models. But little study has been conducted for function-on-function linear regression with (two-way) interaction terms, where the coefficient functions of interactions are three dimensional. We consider function-on-function regression models with interaction effects. For an interaction model with a given form, we propose an estimation method based on the Karhunen-Loeve expansion of the signal function in response curve. In addition to good predictive property, our approach converts the estimation of three dimensional coefficient functions of interaction effects to the estimation of two and one dimensional functions, which greatly improves the computational efficiency. In practice, the forms of models are usually unspecified. We describe a stepwise selection procedure based on our estimation method and a criterion which measures the predictive performance of a model. We examine our proposed methods via simulation and two data sets in ocean environment and air pollution.


Authors who are presenting talks have a * after their name.

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