Inference and martingale estimating equations for stochastic processes on a semigroup (Q1330194)

There are examples where analysis based on ordinary martingales does not appear to lead to optimum estimators. However, if we consider random variables with values in an Abelian semigroup, it is possible to define generalized expectations, generalized additive processes, generalized martingales, and conditional generalized exponential families in an abstract framework. This extension makes it possible to derive generalized martingale estimating equations that provide optimum estimators. Some examples are given to illustrate the theory.