GMM Estimation of Marginal Model with Missing Covariate Data

The multivariate response is commonly seen in longitudinal and cross-sectional design. The marginal model is an important tool in discovering the average influence of the covariates on the response. A main feature of the marginal model is that even without specifying the inter-correlation among different components of the response, we still get consistent estimation of the regression parameters. This paper discusses the GMM estimation of marginal model when the covariates are missing at random. Using the inverse probability weighting and different basic working correlation matrices, we obtain a series of estimating equations. We estimate the parameters of interest by minimizing the corresponding quadratic inference function. Asymptotic normality of the proposed estimator is established. Simulation studies are conducted to investigate the finite sample performance of the new estimator. We also apply our proposal to a real data of mathematical achievement from middle school students.