Additive Function-on-Function Regression

Additive Function-on-Function Regression

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenba...

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Hauptverfasser: Kim, Janet S, Staicu, Ana-Maria, Maity, Arnab, Carroll, Raymond J, Ruppert, David
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Staicu, Ana-Maria
Maity, Arnab
Carroll, Raymond J
Ruppert, David
description We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications.
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title Additive Function-on-Function Regression
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