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Detection of multiple changes in a sequence of dependent variables

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  • Lavielle, Marc

Abstract

We present some results of convergence for a minimum contrast estimator in a problem of change-points estimation. Here, we consider that the changes affect the marginal distribution of a sequence of random variables. We only consider parametric models, but the results are obtained under very general conditions. We show that the estimated configuration of changes converges to the true configuration, and we show that the rate of convergence does not depend on the dependance structure of the process: we obtain the same rate for strongly mixing and strongly dependent processes. When the number of changes is unknown, it is estimated by minimizing a penalized contrast function. Some examples of application to real data are given.

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  • Lavielle, Marc, 1999. "Detection of multiple changes in a sequence of dependent variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 79-102, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:79-102
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    1. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    2. Kim, H. J., 1994. "Likelihood Ratio and Cumulative Sum Tests for a Change-Point in Linear Regression," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 54-70, October.
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