Additive nonlinear functional concurrent model

We propose a flexible regression model to study the association between a functional response and multiple functional covariates that are observed on the same domain. Specifically, we relate the mean of the current response to current values of the covariates by a sum of smooth unknown bivariate functions, where each of the functions depends on the current value of the covariate and the time point itself. In this framework, we develop estimation methodology that accommodates realistic scenarios where the covariates are sampled with or without error on a sparse and irregular design, and prediction that accounts for unknown model correlation structure. We also discuss the problem of testing the null hypothesis that the covariate has no association with the response. The proposed methods are evaluated numerically through simulations and two real data applications.

Keywords

functional concurrent models, F-test, nonlinear models, penalized B-splines, prediction

2010 Mathematics Subject Classification

62G05, 62G10

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Maity’s research was supported by National Institute of Health grant R00 ES017744 and an NCSU Faculty Research and Professional Development grant. Staicu’s research was supported by National Institute of Health grants R01 NS085211 and R01 MH086633 and National Science Foundation grant DMS 1454942.

Received 31 August 2016

Published 19 September 2018