Abstract:
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Sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data. In the present article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace. Our proposal accounts for the covariance structure within each subject and improves efficiency in estimating the central mean subspace if it is correctly specified. Even if it is misspecified, our estimator remains consistent. In addition, our proposal 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 the estimated structural dimension is consistent, and the estimated basis directions are root-n consistent, asymptotically normal and locally efficient. Simulations and an analysis of the Framingham Heart Study data confirm the effectiveness of our proposal.
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