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April 2014 Inverse regression for longitudinal data
Ci-Ren Jiang, Wei Yu, Jane-Ling Wang
Ann. Statist. 42(2): 563-591 (April 2014). DOI: 10.1214/13-AOS1193


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 Ferré 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.


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Ci-Ren Jiang. Wei Yu. Jane-Ling Wang. "Inverse regression for longitudinal data." Ann. Statist. 42 (2) 563 - 591, April 2014.


Published: April 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1296.62073
MathSciNet: MR3210979
Digital Object Identifier: 10.1214/13-AOS1193

Primary: 62G05 , 62G08
Secondary: 62G20

Keywords: Covariance operator , Dimension reduction , Functional data analysis , local polynomial smoothing , regularization , sparse data

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 2 • April 2014
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