## The Annals of Statistics

### 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 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.

#### Article information

Source
Ann. Statist., Volume 42, Number 2 (2014), 563-591.

Dates
First available in Project Euclid: 20 May 2014

https://projecteuclid.org/euclid.aos/1400592170

Digital Object Identifier
doi:10.1214/13-AOS1193

Mathematical Reviews number (MathSciNet)
MR3210979

Zentralblatt MATH identifier
1296.62073

Subjects
Primary: 62G05: Estimation 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

#### Citation

Jiang, Ci-Ren; Yu, Wei; Wang, Jane-Ling. Inverse regression for longitudinal data. Ann. Statist. 42 (2014), no. 2, 563--591. doi:10.1214/13-AOS1193. https://projecteuclid.org/euclid.aos/1400592170

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#### Supplemental materials

• Supplementary material: Supplement to “Inverse regression for longitudinal data”. We provide additional supporting information for Section 2.1, for simulation studies and for data analysis.