Inverse regression for longitudinal data

TL;DR

This paper extends sliced inverse regression to handle intermittently and sparsely measured longitudinal data, providing asymptotic theory, optimal convergence rates, and empirical validation.

Contribution

It introduces a novel sliced inverse regression method tailored for sparse longitudinal data, with theoretical guarantees and practical demonstrations.

Findings

Achieves optimal convergence rates for estimated directions.

Performs well in simulations and real data analysis.

Extends existing methods to handle sparse longitudinal measurements.

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.