Before revision:  which is proved to be able to convert any point within a small but fixed neighborhood of the true parameter value into an estimate that is asymptotically equivalent to GMM. Our result does not require the initial estimate to be consistent and only 2\log n iterations are needed . Since the k-step correction does not require any optimization, applying the k-step correction to MILP estimate provides a computationally attractive way of obtaining efficient estimators.
After revision:  which is proved to be able to convert any point within a small but fixed neighborhood of the true parameter value into an estimate that is asymptotically equivalent to GMM. Our result does not require the initial estimate to be consistent and only 2\log n iterations are needed to obtain an efficient estimator. The overall proposal scales well to handle extremely large sample sizes because lack of consistency requirement allows one to use a very small subsample to obtain the initial estimate and the k-step correction does not require any optimization, applying the k-step correction to MILP estimate provides a computationally attractive way of obtaining efficient estimators.