Nonlinear Function-on-Function Regression Models

• Activity Number: 519
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Noether Award Committee
• Author(s): Arnab Maity*
• Companies: North Carolina State University

Abstract

We propose two flexible regression models to study association between a functional predictor and a functional covariate. First, we develop a general functional concurrent model where the relationship between the mean current response and the covariate is explained by a smooth unknown bi-variate function that depends on both the current value of the covariate and the time point itself. Next, we develop a general function-on-function regression model where the mean current response at a particular time point depends on the time point itself as well as the entire covariate trajectory. For both these models, we develop estimation methodology that accommodates realistic scenarios where the functional covariate is sampled with or without error on a sparse and/or irregular design, and prediction that accounts for unknown model correlation structure. The methodology is flexible and can accommodate multiple scalar or functional predictors. The proposed methods are evaluated numerically through simulations and real data applications.