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Nonanticipating estimation applied to sequential analysis and changepoint detection

Lorden, Gary and Pollak, Moshe (2005) Nonanticipating estimation applied to sequential analysis and changepoint detection. Annals of Statistics, 33 (3). pp. 1422-1454. ISSN 0090-5364. http://resolver.caltech.edu/CaltechAUTHORS:LORas05

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Abstract

Suppose a process yields independent observations whose distributions belong to a family parameterized by theta E Theta. When the process is in control, the observations are i.i.d. with a known parameter value theta(0). 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.


Item Type:Article
Additional Information:© 2005 The Institute of Mathematical Statistics. Received February 2000; revised March 2004. The authors are grateful to the referees and especially to an Associate Editor who gave us one of the most thorough, accurate and helpful reports we have ever received.
Subject Keywords:quality control; cusum; Shiryayev-Roberts; surveillance; statistical process control; power one tests; renewal theory; nonlinear renewal theory; Gamma distribution
Record Number:CaltechAUTHORS:LORas05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LORas05
Alternative URL:http://dx.doi.org/10.1214/009053605000000183
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3881
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Jul 2006
Last Modified:26 Dec 2012 08:56

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