Estimation of Change-Point and Post-Change Means by an Adaptive CUSUM Procedure

• Activity Number: 684
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yanhong Wu*
• Companies: California State University at Stanislaus
• Keywords: Adaptive CUSUM process ; Average run length ; Conditional Bias ; Renewal theory

Abstract

For a sequence of independent normal random variables with pre-change mean 0 and variance 1, an adaptive CUSUM procedure is proposed to detect any parametric post-change means with variance 1 by using the adaptive CUSUM process which consists of a sequence of adaptive sequential tests. An alarm is made when the adaptive CUSUM process crosses the boundary. We first give the asymptotic results for the average in-control and out-of-control run lengths. Then the conditional biases of the change-point and post-change means given the change is detected are studied. Particular attentions are paid to the cases when the post-change mean is a sudden shift or gradually increasing. Nile river flow data and global average temperature data are used for illustration.