Effect of dependence on statistics for determination of change

Antoch, Jaromı́r; Hušková, Marie; Prášková, Zuzana

doi:10.1016/s0378-3758(96)00138-3

Cited by 66 publications

(79 citation statements)

References 12 publications

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“…Typically we set D = R and ∞ n=1 D n = N or Z. See, [5,25,26,34,47,59] for examples of works studying change point detection via increasing domain asymptotics.…”

Section: 1)mentioning

confidence: 99%

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Optimal change point detection in Gaussian processes

Keshavarz

Scott

Nguyen

2018

Journal of Statistical Planning and Inference

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We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed domain (typically arising in spatial data analysis). We propose a detection method based on the generalized likelihood ratio test (GLRT), and show that our method achieves nearly asymptotically optimal rate in the minimax sense, in both settings. The salient feature of the proposed method is that it exploits in an efficient way the data dependence captured by the Gaussian process covariance structure. When the covariance is not known, we propose the plug-in GLRT method and derive conditions under which the method remains asymptotically near optimal. By contrast, the standard CUSUM method, which does not account for the covariance structure, is shown to be asymptotically optimal only in the increasing domain. Our algorithms and accompanying theory are applicable to a wide variety of covariance structures, including the Matern class, the powered exponential class, and others. The plug-in GLRT method is shown to perform well for maximum likelihood estimators with a dense covariance matrix.

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“…Typically we set D = R and ∞ n=1 D n = N or Z. See, [5,25,26,34,47,59] for examples of works studying change point detection via increasing domain asymptotics.…”

Section: 1)mentioning

confidence: 99%

“…there is δ ∈ (0, 2) such that for any k < m, var m j=k X j (m − k + 1) δ . Horváth et al [25,26] and Antoch [5] studied the performance of the CUSUM test for the detection of a sudden change in the mean in linear processes, i.e. X t = ∞ j=0 w j ǫ t−j , in which {ǫ t } ∞ t=−∞ are i.i.d.…”

Section: 1)mentioning

confidence: 99%

Optimal change point detection in Gaussian processes

Keshavarz

Scott

Nguyen

2018

Journal of Statistical Planning and Inference

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“…The estimation of the long-run variance when a change occurs has been addressed in the literature. We follow the approach of Antoch et al (1997), who provided estimators for the long run variance which are asymptotically consistent under the H 0 as well as under the one change alternative. Let x 0 denote the smallest value in [0, 1] where |T n (x)| reaches its maximum and letk = x 0 n .…”

Section: It Follows Immediately That Under the No Change Null Hypothesiŝmentioning

confidence: 99%

Change Point Detection with Stable AR(1) Errors

Bazarova

Berkes

Horváth

2015

Fields Institute Communications

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In this paper we develop two types of tests to detect changes in the location parameters of dependent observations with infinite variances. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. If the d largest (in magnitude) observations are removed from the sample, then the standard CUSUM process developed for weakly dependent observations with finite variance can be used assuming that d = d(n) → ∞ as n, the sample size tends to ∞. We study two types of statistics. The maximally selected CUSUM process we estimate the long run variance by kernel estimators. We also propose ratio statistics which do not depend on the long run variances. Monte Carlo simulations illustrate the the limit results can be used even in case of small and moderate sample sizes.

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“…Not considering the hydro-meteorological impact in DO concentration, and if there are no structural changes in the water quality sources, it is expected that the calibration factor β s,t has no changes over time in its mean. It is applied a statistical test to the filtered predictions of β s,t|t by taking into account that β s,1|1 , β s,2|2 , ..., β s,140|140 are an AR (1) process. [1] shows that when random variables X 1 , X 2 , ..., X n are not independent but form an ARMA sequence then the asymptotic critical values of the test statistics considering independence have to be multiplied by 2π f (0)/γ, where γ = varX t and f (·) denote the special density of the corresponding ARMA process.…”

Section: Change-point Detectionmentioning

confidence: 99%

“…It is applied a statistical test to the filtered predictions of β s,t|t by taking into account that β s,1|1 , β s,2|2 , ..., β s,140|140 are an AR (1) process. [1] shows that when random variables X 1 , X 2 , ..., X n are not independent but form an ARMA sequence then the asymptotic critical values of the test statistics considering independence have to be multiplied by 2π f (0)/γ, where γ = varX t and f (·) denote the special density of the corresponding ARMA process. Especially for an AR(1) sequence, the critical values should be multiplied by (1 + ρ)(1 − ρ) −1 1/2 where ρ is the first autoregressive coefficient, ( [4]).…”

Section: Change-point Detectionmentioning

confidence: 99%

Application of Change-Point Detection to a Structural Component of Water Quality Variables

Gonçalves¹,

Costa²

2011

AIP Conference Proceedings

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Abstract. In this study, methodologies were developed in statistical time series models, such as multivariate state-space models, to be applied to water quality variables in a river basin. In the modelling process it is considered a latent variable that allows incorporating a structural component, such as seasonality, in a dynamic way and a change-point detection method is applied to the structural component in order to identify possible changes in the water quality variables in consideration.

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Effect of dependence on statistics for determination of change

Cited by 66 publications

References 12 publications

Optimal change point detection in Gaussian processes

Optimal change point detection in Gaussian processes

Change Point Detection with Stable AR(1) Errors

Application of Change-Point Detection to a Structural Component of Water Quality Variables

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