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June 2005 Nonanticipating estimation applied to sequential analysis and changepoint detection
Gary Lorden, Moshe Pollak
Ann. Statist. 33(3): 1422-1454 (June 2005). DOI: 10.1214/009053605000000183


Suppose a process yields independent observations whose distributions belong to a family parameterized by θ∈Θ. When the process is in control, the observations are i.i.d. with a known parameter value θ0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37–41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixture-type rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.


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Gary Lorden. Moshe Pollak. "Nonanticipating estimation applied to sequential analysis and changepoint detection." Ann. Statist. 33 (3) 1422 - 1454, June 2005.


Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1077.62067
MathSciNet: MR2195641
Digital Object Identifier: 10.1214/009053605000000183

Primary: 62F03 , 62L10 , 62N10
Secondary: 60K05 , 62F05

Keywords: CUSUM , gamma distribution , nonlinear renewal theory , Power one tests , quality control , renewal theory , Shiryayev–Roberts , statistical process control , surveillance

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 3 • June 2005
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