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Test by adaptive LASSO quantile method for real-time detection of a change-point

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  • Gabriela Ciuperca

    (Université de Lyon, Université Lyon 1)

Abstract

This article proposes a test statistic based on the adaptive LASSO quantile method to detect in real-time a change in a linear model. The model can have a large number of explanatory variables and the errors don’t satisfy the classical assumptions for a statistical model. For the proposed test statistic, the asymptotic distribution under $$H_0$$ H 0 is obtained and the divergence under $$H_1$$ H 1 is shown. It is shown via Monte Carlo simulations, in terms of empirical sizes, of empirical powers and of stopping time detection, that the useful test statistic for applications is better than other test statistics proposed in literature. Two applications on the air pollution and in the health field data are also considered.

Suggested Citation

  • Gabriela Ciuperca, 2018. "Test by adaptive LASSO quantile method for real-time detection of a change-point," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 689-720, August.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:6:d:10.1007_s00184-018-0676-x
    DOI: 10.1007/s00184-018-0676-x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    3. 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.
    4. Li-Ping Zhu & Lin-Yi Qian & Jin-Guan Lin, 2011. "Variable selection in a class of single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1277-1293, December.
    5. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage Estimation Of Regression Models With Multiple Structural Changes," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1376-1433, December.
    6. Zhou, Mi & Wang, Huixia Judy & Tang, Yanlin, 2015. "Sequential change point detection in linear quantile regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 98-103.
    7. Zhu, Li-Ping & Zhu, Li-Xing, 2009. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 862-875, May.
    8. Marie Hušková & Claudia Kirch, 2012. "Bootstrapping sequential change-point tests for linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 673-708, July.
    9. Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
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    Cited by:

    1. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.

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