Detection of structural changes in generalized linear models

Antoch, Jaromı́r; Grègoire, Gèrard; Jarušková, Daniela

doi:10.1016/j.spl.2004.06.028

Cited by 11 publications

(18 citation statements)

References 8 publications

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“…Using the similar arguments as in the proof of Theorem 1, we deduce that the asymptotic distribution of −2 log U ′ 1,n,k1,k2 (β 1 , β 2 ) is χ 2 (3d) and then we can consider the test statistic −2 log U ′ 0,n,k1,k2 (β). We restricted to the case where λ 1 and λ 2 satisfy the constraintṼ 1n (β)λ 1…”

Section: Extension To a Particular Two Change-points Modelmentioning

confidence: 99%

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Empirical likelihood test in a posteriori change-point nonlinear model

Ciuperca

Salloum

2015

Metrika

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In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte-Carlo simulations show the performance of the proposed test statistic, compared to an existing method in literature.

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Section: Extension To a Particular Two Change-points Modelmentioning

confidence: 99%

“…i,jk = β 0 + v i,jk (β − β 0 ), with u i,jk , v i,jk ∈ [0, 1]. We note that β (1) i,jk and β (2) i,jk are random vectors which depend on X i . For .…”

Section: Appendixmentioning

confidence: 99%

Empirical likelihood test in a posteriori change-point nonlinear model

Ciuperca

Salloum

2015

Metrika

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“…Both models are continuous at the change point, and the hinge model is a special case of the segmented model by assuming zero slope before the threshold. Much work has been done regarding hypothesis testing in threshold models (e.g., Davies, 1987;Ulm, 1991;Koziol and Wu, 1996;Xu and Adak, 2002;Mazumdar et al, 2003;Pastor-Barriuso et al, 2003;Antoch et al, 2004;Zheng and Chen, 2005;Gurevich, 2006, 2009;Lee et al, 2011). Our goal in this article is to develop model-robust methods for constructing confidence intervals for coefficients in continuous threshold models, which should provide proper coverage even when the true underlying model differs from the assumed model.…”

Section: Introductionmentioning

confidence: 99%

Model-Robust Inference for Continuous Threshold Regression Models

Fong

Huang

et al. 2016

Biometrics

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Summary We study threshold regression models that allow the relationship between the outcome and a covariate of interest to change across a threshold value in the covariate. In particular we focus on continuous threshold models, which experience no jump at the threshold. Continuous threshold regression functions can provide a useful summary of the association between outcome and the covariate of interest, because they offer a balance between flexibility and simplicity. Motivated by collaborative works in studying immune response biomarkers of transmission of infectious diseases, we study estimation of continuous threshold models in this paper with particular attention to inference under model misspecification. We derive the limiting distribution of the maximum likelihood estimator, and propose both Wald and test-inversion confidence intervals. We evaluate finite sample performance of our methods, compare them with bootstrap confidence intervals, and provide guidelines for practitioners to choose the most appropriate method in real data analysis. We illustrate the application of our methods with examples from the HIV-1 immune correlates studies.

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“…Antoch et al (2004) considered the structural changes (retrospective or a posteriori tests) based on ML scores in generalized linear models and obtained Darling-Erdös type limit distribution. In this article, we monitor structural changes in generalized linear models (sequential or a priori tests) and develop quite different asymptotic theories from those proposed by Antoch et al (2004). Our developments include asymptotic distributions of the test statistics under null hypothesis, the asymptotic crossing probability in multi-dimension case, and the estimation of detection delay.…”

Section: Introductionmentioning

confidence: 99%

“…Bauer and Hackl (1978) proposed a MOSUM test based on moving sums of recursive residuals which was extended to linear models by Chu et al (1995). The above literatures focus on retrospective or a posteriori tests and most of them on linear models except for Antoch et al (2004).…”

Section: Introductionmentioning

confidence: 99%

Monitoring Structural Changes in Generalized Linear Models

Xia

Peng-jiang

Zhao

2009

Communications in Statistics - Theory and Methods

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In this article, we introduce two monitoring schemes to (sequentially) detect structural changes in generalized linear models and develop asymptotic theories for them. The first method is based on cumulative sums (CUSUM) of weighted residuals, in which the unknown in-control parameters have been replaced by its maximum likelihood (ML) estimate from the training sample, whereas the second scheme makes use of moving sums (MOSUM) of weighted residuals. We characterize the limit distribution of the test statistic and show that these tests are consistent. Moreover, we also obtain and tabulate the asymptotic critical values of the tests. Finally, we study the speed of detection under different conditions. The methods are illustrated and compared in several simulations.

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Detection of structural changes in generalized linear models

Cited by 11 publications

References 8 publications

Empirical likelihood test in a posteriori change-point nonlinear model

Empirical likelihood test in a posteriori change-point nonlinear model

Model-Robust Inference for Continuous Threshold Regression Models

Monitoring Structural Changes in Generalized Linear Models

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