Estimating equations

Summary

The method of estimating equations defines an estimator as a solution of $\sum_i g(X_i, \theta) = 0$. Here the function $g$ has mean zero at the true parameter. The likelihood equations, the moment equations of the method of moments and the normal equations of least squares are all estimating equations. The approach needs only a model for some moments, not a full probability model. Its asymptotic theory is the same as that of M-estimators, with a sandwich formula for the variance.