title: An estimating equation approach to dimension reduction for longitudinal data.
abstract: Sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data. In this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace. The proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified. Even if the covariance structure is misspecified, our estimator remains consistent. In addition, our method relaxes distributional assumptions on the covariates and is doubly robust. To determine the structural dimension of the central mean subspace, we propose a Bayesian-type information criterion. We show that the estimated structural dimension is consistent and that the estimated basis directions are root-[Formula: see text] consistent, asymptotically normal and locally efficient. Simulations and an analysis of the Framingham Heart Study data confirm the effectiveness of our approach.
authors.affiliation: State Key Laboratory of Genetic Engineering, School of Life Sciences, Fudan University, 2005 Songhu Road, Shanghai 200438, China , kelinxu12@fudan.edu.cn.
authors.forename: Kelin
authors.initials: K
authors.lastname: Xu
authors.affiliation: Division of Biostatistics, University of Pennsylvania, 423 Guardian Drive, Philadelphia, Pennsylvania 19104, U.S.A.
authors.forename: Wensheng
authors.initials: W
authors.lastname: Guo
authors.affiliation: Division of Biostatistics, Human Genetics Center, The University of Texas Health Science Center at Houston, 1200 Herman Pressler, Houston, Texas 77030, U.S.A. , momiao.xiong@uth.tmc.edu.
authors.forename: Momiao
authors.initials: M
authors.lastname: Xiong
authors.affiliation: Institute of Statistics and Big Data, Renmin University of China, 59 Zhongguancun Avenue, Beijing 100872, China , zhu.liping@mail.shufe.edu.cn.
authors.forename: Liping
authors.initials: L
authors.lastname: Zhu
authors.affiliation: State Key Laboratory of Genetic Engineering, School of Life Sciences, Fudan University, 2005 Songhu Road, Shanghai 200438, China , lijin@fudan.edu.cn.
authors.forename: Li
authors.initials: L
authors.lastname: Jin
keywords: Central mean subspace; Dimension reduction; Estimating equation; Longitudinal data; Semiparametric efficiency; Sliced inverse regression