Abstract
We investigate the problem of testing for a change-point in stationary statistical models and of estimating the change parameters in an off-line framework. This paper provides asymptotic results which emphasize the need for weighting the classical test statistics when the change time is completely unknown. The asymptotic expansions can also give new detectors which are simpler for using.
First, we present the different models under investigation (§I) and the corresponding tests (§II). The third paragraph will be devoted to the different ways for comparing these tests -both asymptotic and non asymptotic ones- and the partial results we can give. The fourth part is central: it proves the need for normalizing the test statistics near the edges of the observation window and contains the application on three well-known time-series. The last paragraph details the asymptotic tools used before: invariance theorems for the likelihood ratio process provide the asymptotic behaviour of the test statistics and the asymptotic distribution of the estimators of a change.
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Deshayes, J., Picard, D. (1985). Off-line statistical analysis of change-point models using non parametric and likelihood methods. In: Basseville, M., Benveniste, A. (eds) Detection of Abrupt Changes in Signals and Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006392
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DOI: https://doi.org/10.1007/BFb0006392
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