Quasi-stationary biases of change point and change magnitude estimation after sequential cusum test

Abstract

Assuming the observation process is a Brownian motion with the drift parameter subject to sudden change, estimations of the change point and change magnitude after the sequential CUSUM test are proposed and investigated. By assuming that the change occures far away from 0, the biases of the estimations conditioning on that the change is detected are obtained as the control limit approaches infinity

Keywords:

• Bias reduction
• Brownian motion
• Change point problem