A weighted estimating equation for missing covariate data with properties similar to maximum likelihood

In regression analysis, missing covariate data occurs often. A recent approach to analyzing such data is weighted estimating equations. With weighted estimating equations, the contribution to the estimating equation from a complete observation is weighted by the inverse probability of being observed. In this article we propose a weighted estimating equation that is almost identical to the maximum likelihood estimating equations. As such, we propose an EM-type algorithm to solve these weighted estimating equations. Although the weighted estimating equations are a special case of those proposed earlier by Robins et al., our EM-type algorithm to solve them is new. Similar to Robins and Ritov, we give the result that to obtain a consistent estimate of the regression parameters, either the missing-data mechanism or the distribution of thr missing data given the observed data must be correctly specified. We compare the weighted estimating equations to maximum likelihood via two examples, a simulation and an asymptotic study.