A REVIEW OF SOME ASPECTS OF ASYMPTOTIC LIKELIHOOD THEORY FOR STOCHASTIC-PROCESSES

Some important aspects of the asymptotic likelihood theory for stochas tic processes is reviewed, with particular attention to martingale pro perties and to information and higher order likelihood quantities. Int errelations between those quantities are discussed. Furthermore, resul ts are given on the asymptotic distribution of the score function and the maximum likelihood estimator when standardized by the various info rmation matrices. Model robust procedures for constructing confidence regions are considered, and a robust measure of information is discuss ed in some detail. Finally, extensions of the ideas to estimating equa tions are considered. Throughout the theory is illustrated by examples .