Inverse Regression for Functional and Longitudinal Data

Abstract

Sliced inverse regression is an appealing dimension reduction method that was developed for regression models with multivariate covariates. The aim of this talk is to extend it to both functional and intermittently measured longitudinal covariates. Previous work in dimension reduction with functional covariates concentrates on the case where the whole trajectories of random functional covariates are assumed to be observed completely. Our approach allows for longitudinal covariates that are recorded discretely and intermittently. We develop asymptotic theory for the new procedure and show that the effective dimension reduction space can be estimated at the root-n rate of convergence. The effectiveness of the approach is demonstrated through a fecundity data of Medflies.