Asymptotic Likelihood Theory

Here we discuss the asymptotic likelihood theory for stochastic processes following Barndorff-Nielsen and Sorensen [3] and Kuchler and Sorensen [13]. It is well known that the Fisher information plays a major role in the asymptotic theory of statistical inference for stochastic processes. For instance, see [4]. The score function is standardized using the information, and the asymptotic normality of the maximum likelihood estimator is investigated. The information used for normalization could be either the observed information or the expected information depending on the nature of the problem. In addition to the observed and the expected information, we consider two additional information measures, which will be called incremental observed information and incremental expected information in the general context of stochastic processes.