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The lasso for high dimensional regression with a possible change point

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  • Sokbae Lee
  • Myung Hwan Seo
  • Youngki Shin

Abstract

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l1 estimation loss for regression coefficients. Since the Lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold e ect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a nearly n-1 factor even when the number of regressors can be much larger than the sample size (n). We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.
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  • 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.
    • Handle: RePEc:bla:jorssb:v:78:y:2016:i:1:p:193-210
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    3. A. Gibberd & S. Roy, 2021. "Consistent multiple changepoint estimation with fused Gaussian graphical models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 283-309, April.
    4. Abhimanyu Gupta & Myung Hwan Seo, 2023. "Robust Inference on Infinite and Growing Dimensional Time‐Series Regression," Econometrica, Econometric Society, vol. 91(4), pages 1333-1361, July.
    5. Yang, Xinfeng & Yan, Xiaodong & Huang, Jian, 2019. "High-dimensional integrative analysis with homogeneity and sparsity recovery," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    6. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1511-1543.
    7. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    8. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.
    9. Yoici Arai & Taisuke Otsu & Myung Hwan Seo, 2019. "Causal inference on regression discontinuity designs by high-dimensional methods," STICERD - Econometrics Paper Series 601, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Okui, Ryo & Wang, Wendun, 2021. "Heterogeneous structural breaks in panel data models," Journal of Econometrics, Elsevier, vol. 220(2), pages 447-473.
    11. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2018. "Oracle Estimation of a Change Point in High-Dimensional Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1184-1194, July.
    12. Alessandro Casini & Pierre Perron, 2018. "Continuous Record Asymptotics for Change-Points Models," Papers 1803.10881, arXiv.org, revised Nov 2021.
    13. 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.
    14. Daiqing Xi & Tianxiao Pang, 2021. "Estimating multiple breaks in mean sequentially with fractionally integrated errors," Statistical Papers, Springer, vol. 62(1), pages 451-494, February.
    15. Laurent Callot & Mehmet Caner & Anders Bredahl Kock & Juan Andres Riquelme, 2017. "Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 250-264, April.
    16. Kapetanios, George & Zikes, Filip, 2018. "Time-varying Lasso," Economics Letters, Elsevier, vol. 169(C), pages 1-6.
    17. Zhao, Wenbiao & Zhu, Lixing, 2024. "Detecting change structures of nonparametric regressions," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    18. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    19. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    20. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    21. repec:ags:aaea22:335707 is not listed on IDEAS
    22. Xu, Haotian & Wang, Daren & Zhao, Zifeng & Yu, Yi, 2022. "Change point inference in high-dimensional regression models under temporal dependence," LIDAM Discussion Papers ISBA 2022027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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