Inverse regression for longitudinal data
Abstract
Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method.
Cite
@article{arxiv.1405.6017,
title = {Inverse regression for longitudinal data},
author = {Ci-Ren Jiang and Wei Yu and Jane-Ling Wang},
journal= {arXiv preprint arXiv:1405.6017},
year = {2015}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Corrections