Robust estimating equations and bias correction of correlation parameters for longitudinal data

The estimation of correlation parameters has received attention for both its own interest and improvement of the estimation efficiency of mean parameters by the generalized estimating equations (GEE) approach. Many of the well-established methods for the estimation of correlation parameters can be constructed under the GEE framework which is, however, sensitive to outliers. In this paper, we consider two ways of constructing robust estimating equations for achieving robust estimation of the correlation parameters. Furthermore, the estimators of the correlation parameters from the robustified GEE may be still biased as the expectation of the estimating equation is biased from zero when the underlying distribution is not symmetric. Therefore, bias-corrected robust estimators of correlation parameters are proposed. The performance of the proposed methods are investigated by simulation. The results show that the proposed robust and bias-corrected robust estimators can reduce the bias successfully. Two real data sets are analyzed for illustration.