On asymptotics of estimating functions

The asymptotic theory of estimators obtained from estimating functions is re-viewed and some new results on the multivariate parameter case are presented. Specifically, results about existence of consistent estimators and about asymptotic normality of these are given. First a very general stochastic process setting is considered. Then it is demonstrated how more specific conditions for existence of√ n-consistent and asymptotically normal estimators can be given for martingale estimating functions in the case of observations of a Markov process. Key words: asymptotic normality, consistency, diffusion processes, estimating equations, likelihood inference, Markov processes, martingale estimating functions, misspecified models, statistical inference for stochastic processes, quasi likelihood. ∗MaPhySto- Centre for Mathematical Physics and Stochastics, funded by a grant from The Danis