Brownian bridge hypothesis testing for the initial transient problem

This paper models the detection of the initial transient in a steady-state simulation problem as a change point hypothesis testing problem. We introduce two new hypothesis tests for the initial transient, each of which is based on the Brownian bridge process and each of which is a composite test that involves testing against infinitely many alternatives (that depend on the duration of the transient period). One of our two procedures is closely related to the class of tests proposed by Schruben, Singh, and Tierney (1983).