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.
Publié le : 2005-06-14
Classification:
Quality control,
cusum,
Shiryayev–Roberts,
surveillance,
statistical process control,
power one tests,
renewal theory,
nonlinear renewal theory,
Gamma distribution,
62L10,
62N10,
62F03,
62F05,
60K05
@article{1120224108,
author = {Lorden, Gary and Pollak, Moshe},
title = {Nonanticipating estimation applied to sequential analysis and changepoint detection},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 1422-1454},
language = {en},
url = {http://dml.mathdoc.fr/item/1120224108}
}
Lorden, Gary; Pollak, Moshe. Nonanticipating estimation applied to sequential analysis and changepoint detection. Ann. Statist., Tome 33 (2005) no. 1, pp. 1422-1454. http://gdmltest.u-ga.fr/item/1120224108/