Oe. Barndorffnielsen et M. Sorensen, A REVIEW OF SOME ASPECTS OF ASYMPTOTIC LIKELIHOOD THEORY FOR STOCHASTIC-PROCESSES, International statistical review, 62(1), 1994, pp. 133-165
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
.