A0825
Title: Concurrent object regression
Authors: Satarupa Bhattacharjee - Pennsylvania State University (United States) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations. Examples of such data objects include covariance matrices, graph Laplacians of networks, and univariate probability distribution functions. A new concurrent Frechet regression model is proposed to characterize the time-varying relation between an object in a general metric space (as a response) and a multivariate real-valued vector (as a predictor). Concurrent regression has been a well-studied area of research for Euclidean predictors and responses, with many important applications for longitudinal studies and functional data. Generalized versions of global least squares regression and locally weighted least squares smoothing, both in the context of concurrent regression for responses situated in general metric spaces, are developed. Estimators that can accommodate sparse and/or irregular designs are proposed. Consistency results are demonstrated for the sample estimates towards appropriate population targets along with the corresponding rates of convergence. The proposed models are illustrated with mortality data and resting state functional Magnetic Resonance Imaging data (fMRI) as responses.
