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A general criterion to determine the number of change-points

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  • Ciuperca, Gabriela

Abstract

A general criterion is proposed to determine the number K of the change-points in a parametric nonlinear multi-response model. Schwarz criterion is a particular case. The change-points depend on regressor values and not on instant of measure. We prove that the proposed estimator for K is consistent. Simulation results, using Monte Carlo technique, for nonlinear models which have numerous applications, support the relevance of the theory.

Suggested Citation

  • Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1267-1275
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    References listed on IDEAS

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    1. Ciuperca, Gabriela, 2009. "The M-estimation in a multi-phase random nonlinear model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 573-580, March.
    2. Wu, Y., 2008. "Simultaneous change point analysis and variable selection in a regression problem," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2154-2171, October.
    3. Konrad Nosek, 2010. "Schwarz information criterion based tests for a change-point in regression models," Statistical Papers, Springer, vol. 51(4), pages 915-929, December.
    4. Pan, Jianmin & Chen, Jiahua, 2006. "Application of modified information criterion to multiple change point problems," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2221-2241, November.
    5. Gabriela Ciuperca, 2011. "Penalized least absolute deviations estimation for nonlinear model with change-points," Statistical Papers, Springer, vol. 52(2), pages 371-390, May.
    6. Gabriela Ciuperca, 2011. "Estimating nonlinear regression with and without change-points by the LAD method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 717-743, August.
    7. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    8. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
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    1. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.
    2. David Ardia & Arnaud Dufays & Carlos Ordás Criado, 2024. "Linking Frequentist and Bayesian Change-Point Methods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1155-1168, October.
    3. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    4. Kang-Ping Lu & Shao-Tung Chang, 2021. "Robust Algorithms for Change-Point Regressions Using the t -Distribution," Mathematics, MDPI, vol. 9(19), pages 1-28, September.
    5. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.
    6. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.

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