Generalized Functional Latent Feature Models with Single-Index Interactions

• Activity Number: 272
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Raymond Carroll*+ and Yehua Li and Naisyin Wang
• Companies: Texas A&M University and The University of Georgia and University of Michigan
• Keywords: Single index models ; Nonparametric regression ; Semiparametric regression ; Interactions ; Latent Features

Abstract

We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single-index structure. We propose a two step estimation procedure based on local estimating equations, and investigate two situations: (a) when the basis functions are pre-determined, e.g., Fourier or wavelet basis functions and the functional features of interest are known; and (b) when the basis functions are data driven, such as with functional principal components. Asymptotic properties are developed, and an example discussed.