By the law of large numbers, formula_3 for large values of "T", and thus we expect that formula_4. The generalized method of moments looks for a number formula_5 which would make formula_6 as close to zero as possible. Mathematically, this is equivalent to minimizing a certain norm of formula_7 (norm of "m", denoted as ||"m"||, measures the distance between "m" and zero). The properties of the resulting estimator will depend on the particular choice of the norm function, and therefore the theory of GMM considers an entire family of norms, defined as