Efficient estimation for time-dynamic longitudinal single-index model

Shu Liu and Liangyuan Liu

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 15, 3656-3674

Abstract: We study the efficient estimation procedure of a new single-index model which can reflect the time-dynamic effects for longitudinal covariates. We propose a efficient estimator of the single-index parameter by using a feasible bias-corrected generalized estimating equation. In order to achieve this goal, we use the working independence estimator as an initial estimation, and then a non parametric smoothing technique is used to model the covariance matrix. With appropriate initial estimates of the parametric index, the proposed estimators are shown to be n$\sqrt{n}$-consistent and asymptotically normally distributed, and the two-stage estimator is shown to be more efficient than the first-stage estimator. We also address the non parametric estimation of regression functions and provide estimates with optimal convergence rates. The finite-sample properties of the estimator are illustrated by some simulation examples, as well as a real data application.

Date: 2018
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DOI: 10.1080/03610926.2017.1361986

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