title: Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.
abstract: We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials.
authors.affiliation: Cornell University.
authors.forename: Dawn B
authors.initials: DB
authors.lastname: Woodard
authors.forename: Ciprian
authors.initials: C
authors.lastname: Crainiceanu
authors.forename: David
authors.initials: D
authors.lastname: Ruppert
keywords: Functional data analysis; Lévy adaptive regression kernels; electroencephalogram; functional linear model; kernel mixture; nonparametric Bayes