Online Program Home
My Program

Abstract Details

Activity Number: 176
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #320369
Title: Nonlinear Function on Function Regression with Multiple Prediction Curves
Author(s): Xin Qi* and Ruiyan Luo
Companies: Georgia State University and
Keywords: nonlinear function on function regression ; multiple prediction curves ; Karhunen-Loeve expansion ; generalized functional eigenvalue problem ; penalized eigenvalue problem ; Asymptotic theory

We consider a class of nonlinear function on function regression models with multiple prediction curves. Compared to the linear function-on-function regression model which contains the sum of integrals of the products of the prediction curves and the corresponding coefficient kernel functions, we have the sum of integrals of unknown nonlinear functions of the individual prediction functions and corresponding time arguments. Inspired by the Karhunen-Loeve decomposition of the signal part of the response function, we provide expansions of the nonlinear functions which have the minimum prediction error in a large class of expansions. A generalized functional eigenvalue problem is proposed to estimate the expansions with penalties imposed to control the number of terms in the expansion and the smoothness of the estimated functions. Algorithms have been proposed to solving the penalized eigenvalue problem. Asymptotic theory for our estimation is provided.

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

Back to the full JSM 2016 program

Copyright © American Statistical Association