Title:
Inference for Change-Point and Post-Change Mean with Possible Change in VarianceAuthors:
Yanhong Wu1 ywu@pacific.eduSource:
Sequential Analysis; Aug2005, Vol. 24 Issue 3, p279-302, 24p, 2 chartsDocument Type:ArticleSubject Terms:*
MATHEMATICS
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ESTIMATION theory
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LEAST squares
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MATHEMATICAL statistics
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STOCHASTIC processesAuthor-Supplied Keywords:
Biased estimation
Change-point problem
Corrected confidence interval
CUSUM procedure
Random walk theory
Renewal theoremAbstract:For a sequence of independent normal random variables, we consider the estimation of the change-point and the post-change mean after a change in the mean is detected by a CUSUM procedure, subject to a possible change in variance. Conditional on the event that a change is detected and it occurred far away from the starting point and the threshold is large, the (absolute) bias of the maximum likelihood estimator for the change-point (obtained at the reference value) is found. The first-order biases for the post-change mean and variance estimators are also obtained by using Wald's Likelihood Ratio Identity and the renewal theorem. In the local case when the reference value and the post-change mean are both small, accurate approximations are derived. A confidence interval for post-change mean based on a corrected normal pivot is then discussed. [ABSTRACT FROM AUTHOR]
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