A Change-point Connection to the Marginal Standard Error Rule for Initial Transient Deletion

R. J. Wang and P. W. Glynn

Submitted for publication.

In this paper, we prove that the marginal standard error rule (MSER) for deleting the initial transient in a steady-state simulation is almost surely equal, as the simulated time horizon tends to infinity, to the minimizer of a statistic that arises naturally in the theory of change-point problems, specifically one involving cumulative sum (CUSUM) hypothesis tests. In addition, we prove that MSER deletes the theoretically correct initial transient in two queueing settings in which strong initial transients are present. Numerical results illustrate our findings.