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684 – Stochastic Processes in Computation and Inference
Estimation of Change-Point and Post-Change Means by an Adaptive CUSUM Procedure
Yanhong Wu
California State University, Stanislaus
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.