Estimating with partial statistics the parameters of ergodic finite Markov sources

Parameter estimation based on data emitted from a finite ergodic Markov source is discussed. This can be considered an extension of the memoryless case. First, an asymptotically optimal estimator is suggested for the case where the parametric model is completely known. For an unknown parametric model (e.g unknown noise distribution with training sequences available) a necessary condition is given for the existence of a universally optimum estimate. A universal estimate is then suggested that is asymptotically nearly optimal. The results hold under fairly mild regularity conditions