8,095 research outputs found
Inverse regression for longitudinal data
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.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). With Correction
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