Generalising the Generalised Method of Moments

The original research paper which presented the Generalised Method of Moments was set in reasonably abstract terms, using mathematical tools such as separable metric spaces and open sets. The abstraction is a good idea, as it puts the theory in a wider context than its immediate statistical application. Theorems in the paper describe the behaviour of two key parameters in a particular minimised function. These results are part of a much wider theory of parameter distribution in minimised functionals, including Noether's theorem which is important in the Risk Symmetries described previously in this blog.