The initial transient in steady-state point estimation: Contexts, a bibliography, the mse criterion, and the MSER statistic

The initial transient is an unavoidable issue when estimating parameters of steady-state distributions. We discuss contexts and factors that affect how the initial transient is handled, provide a bibliography (from the system simulation literature), discuss criteria for evaluating initial-transient algorithms, arguing for focusing on the mean squared error (mse). We discuss the MSER statistic, showing that it is asymptotially proportional to the mse and therefore a good foundation for initial-transient algorithms. We suggest two new algorithms (MSER-LLM and MSER-LLM2) for using the MSER statistic and compare them, based on empirical results for M/M/1 and AR(1) data processes, to the original MSER algorithm (MSER-GM).