Mathematics – Statistics Theory
Scientific paper
2005-07-21
Annals of Statistics 2005, Vol. 33, No. 3, 1422-1454
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053605000000183 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053605000000183
Suppose a process yields independent observations whose distributions belong to a family parameterized by \theta\in\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.
Lorden Gary
Pollak Moshe
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