GEE analysis for longitudinal single-index quantile regression

- Proposed GEE methodology to incorporate correlation in quantile single-index models.
- Proved that smoothed GEE results in estimators that are asymptotically as efficient as the original GEE estimator.
- Numerically demonstrated the advantage of incorporating correlation.

We consider a single-index quantile regression model for longitudinal data. Based on generalized estimating equations, an estimation procedure is proposed by taking into account the correlation within subject. Under mild assumptions, we derive the convergence rate of the estimator of the unknown link function and the asymptotic normality of estimator of the index parameter using the “projection” technique. Since the estimating equations are non-continuous, we further adopt the smoothing approach and show that estimators obtained from the smoothed estimating equations are asymptotically equivalent to that from the unsmoothed estimating equations. It is also shown that the estimator is more efficient when the correlation is correctly specified. Finally, we present numerical examples including simulations and analysis of a lung function data.