Sequential Changepoint Detection in Quality Control and Dynamical Systems

Lai, Tze Leung

doi:10.1111/j.2517-6161.1995.tb02052.x

Cited by 425 publications

(297 citation statements)

References 67 publications

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“…In the seminal paper of Lai [17], classical sequential change detection schemes were extended to the AR(p) model involving nuisance parameters. There are similarities between his approach and ours.…”

Section: Testmentioning

confidence: 99%

“…As tests in [17] are the only ones that we found that perform sequential tests of change in the same generality, in [23] extensive numerical comparisons were done with those only. The main conclusion is that no matter when the change occurs, the new procedure has an acceptable empirical level, whereas the algorithm of [17], and other similar optimal procedures, that control the expected value of the stopping time under H 0 , can have unacceptably high type I error probability if the change is not soon after monitoring begins.…”

Section: Testmentioning

confidence: 99%

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Monitoring parameter change in AR(p) time series models

Gombay

Șerban

2009

Journal of Multivariate Analysis

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a b s t r a c t Sequential tests that are generalizations of Page's CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to the efficient score vector under the null hypothesis of no change and under the alternative. The empirical power of the tests is evaluated in a simulation study. The new method performs better than the existing ones found in the literature if the criterion is the type I error probability, which can be unacceptably high for methods that minimize the expected value of the reaction time.

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Section: Testmentioning

confidence: 99%

Section: Testmentioning

confidence: 99%

Monitoring parameter change in AR(p) time series models

Gombay

Șerban

2009

Journal of Multivariate Analysis

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“…There is an extensive literature on the subject of quick detection of changes in the parameters of a model of a stochastic system on the basis of sequential observations of the system, see for instance Lai (1995), and references therein. The simplest case of this problem can be described as follows.…”

Section: Introductionmentioning

confidence: 99%

An objective Bayesian analysis of the change point problem

Moreno

Casella

Garcı́a-Ferrer

2005

Stoch Environ Res Ris Assess

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The Bayesian literature on the change point problem deals with the inference of a change in the distribution of a set of time-ordered data based on a sample of fixed size. This is the so-called ''retrospective or off-line'' analysis of the change point problem. A related but different problem is that of the ''sequential'' change point detection, mainly analyzed from a frequentist viewpoint. While the former typically focuses on the estimation of the position in which the change point occurs, the latter is a testing problem which has a natural formulation as a Bayesian model selection problem. In this paper we provide such a Bayesian formulation, which generalizes previous formulations such as the well-known CUSUM stopping rule. We show that the conventional improper priors (also called non-informative, objective or default), cannot be used either for sequential detection of the change or for retrospective estimation. Then, we propose objective intrinsic prior distributions for the unknown model parameters. The normal and Poisson cases are studied in detail and examples with simulated and real data are provided.

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“…For continuous time this result was recently obtained by Shiryaev (1996). Lai (1995Lai ( , 1998 and Lai and Shan (1999) considered the change-point problem in the more general situation of dependent random variables. In Lai (1995), it was shown that the Neyman-Pearson type procedure with the "moving window" of observations is asymptotically optimal.…”

mentioning

confidence: 99%

“…Lai (1995Lai ( , 1998 and Lai and Shan (1999) considered the change-point problem in the more general situation of dependent random variables. In Lai (1995), it was shown that the Neyman-Pearson type procedure with the "moving window" of observations is asymptotically optimal. In Lai (1998) different boundaries for the "false alarm" probability were introduced instead of upper boundaries for the average time before the "false alarm" and the asymptotic optimality of Page's CUSUM method was proved.…”

mentioning

confidence: 99%