Asymptotic properties of maximum likelihood estimators from dependent observations (Q1082739)

The author considers the case when the log-likelihood functions satisfy some martingale. Under the regularity conditions, it is shown from the inverse function theorem that the likelihood equations have a unique consistent solution, and also that the maximum likelihood estimator is asymptotically normally distributed and is first order efficient. The conditions are analogous to those of \textit{M. J. Crowder}, J. R. Stat. Soc., Ser. B 38, 45-53 (1976; Zbl 0324.62023). A similar result in the i.i.d. case was given by \textit{R. V. Foutz}, J. Am. Stat. Assoc. 72, 147- 148 (1977; Zbl 0354.62029).