In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.
Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
It can be shown that taking will result in the most efficient estimator in the class of all asymptotically normal estimators.
Another important issue in implementation of minimization procedure is that the function is supposed to search through (possibly high-dimensional) parameter space Θ and find the value of θ which minimizes the objective function.No generic recommendation for such procedure exists, it is a subject of its own field, numerical optimization.When the number of moment conditions is greater than the dimension of the parameter vector θ, the model is said to be over-identified.Over-identification allows us to check whether the model's moment conditions match the data well or not.Consistency is a statistical property of an estimator stating that, having a sufficient number of observations, the estimator will converge in probability to the true value of parameter: The second condition here (so-called Global identification condition) is often particularly hard to verify.
There exist simpler necessary but not sufficient conditions, which may be used to detect non-identification problem: Asymptotic normality is a useful property, as it allows us to construct confidence bands for the estimator, and conduct different tests.
Often, time-to-event or survival data are gathered at particular observation times.
A physician will detect the recurrence of cancer only when there is a follow-up ap...
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The method requires that a certain number of moment conditions were specified for the model.