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Simultaneous change point analysis and variable selection in a regression problem

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  • Wu, Y.

Abstract

In this paper, an information-based criterion is proposed for carrying out change point analysis and variable selection simultaneously in linear models with a possible change point. Under some weak conditions, this criterion is shown to be strongly consistent in the sense that with probability one, it chooses the smallest true model for large n. Its byproducts include strongly consistent estimates of the regression coefficients regardless if there is a change point. In case that there is a change point, its byproducts also include a strongly consistent estimate of the change point parameter. In addition, an algorithm is given which has significantly reduced the computation time needed by the proposed criterion for the same precision. Results from a simulation study are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:2154-2171
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    2. 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.
    3. Yongjun Li & Xiao Shi & Min Yang & Liang Liang, 2017. "Variable selection in data envelopment analysis via Akaike’s information criteria," Annals of Operations Research, Springer, vol. 253(1), pages 453-476, June.
    4. Shohoudi, Azadeh & Khalili, Abbas & Wolfson, David B. & Asgharian, Masoud, 2016. "Simultaneous variable selection and de-coarsening in multi-path change-point models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 202-217.
    5. Zhao, Wenbiao & Zhu, Lixing, 2024. "Detecting change structures of nonparametric regressions," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    6. Gabriela Ciuperca, 2014. "Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(2), pages 349-374, May.
    7. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.

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