Optimal Penalized Function-on-Function Regression under a Reproducing Kernel Hilbert Space Framework.

ABSTRACT: Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we present in this paper a function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form of penalized least squares where the penalty enforces a certain level of smoothness on the estimator. Our first result is the Representer Theorem which states that the exact optimizer of the penalized least squares actually resides in a data-adaptive finite dimensional subspace although the optimization problem is define

SUBMITTER: Sun X 

PROVIDER: S-EPMC6380514 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature