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February 2011 Functional single index models for longitudinal data
Ci-Ren Jiang, Jane-Ling Wang
Ann. Statist. 39(1): 362-388 (February 2011). DOI: 10.1214/10-AOS845


A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With appropriate initial estimates of the parametric index, the proposed estimator is shown to be $\sqrt{n}$-consistent and asymptotically normally distributed. We also address the nonparametric estimation of regression functions and provide estimates with optimal convergence rates. One advantage of the new approach is that the same bandwidth is used to estimate both the nonparametric mean function and the parameter in the index. The finite-sample performance for the proposed procedure is studied numerically.


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Ci-Ren Jiang. Jane-Ling Wang. "Functional single index models for longitudinal data." Ann. Statist. 39 (1) 362 - 388, February 2011.


Published: February 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1209.62073
MathSciNet: MR2797850
Digital Object Identifier: 10.1214/10-AOS845

Primary: 62G05 , 62G08
Secondary: 62G20

Keywords: Asymptotic theory , cross-validation , Dimension reduction , functional data , MAVE , smoothing

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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