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The lasso for high-dimensional regression with a possible change-point

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  • Sokbae (Simon) Lee

    (Institute for Fiscal Studies and Columbia University)

  • Myung Hwan Seo

    (Institute for Fiscal Studies)

  • Youngki Shin

    (Institute for Fiscal Studies)

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.

Suggested Citation

  • Sokbae (Simon) Lee & Myung Hwan Seo & Youngki Shin, 2014. "The lasso for high-dimensional regression with a possible change-point," CeMMAP working papers CWP26/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:26/14
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    1. anonymous, 1995. "Does the bouncing ball lead to economic growth?," Regional Update, Federal Reserve Bank of Atlanta, issue Jul, pages 1-2,4-6.
    2. 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.
    3. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    4. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    5. Harchaoui, Z. & Lévy-Leduc, C., 2010. "Multiple Change-Point Estimation With a Total Variation Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1480-1493.
    6. Jelena Bradic & Jianqing Fan & Weiwei Wang, 2011. "Penalized composite quasi‐likelihood for ultrahigh dimensional variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 325-349, June.
    7. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-384, Oct.-Dec..
    8. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 177-218.
    9. Pesaran, M. Hashem & Pick, Andreas, 2007. "Econometric issues in the analysis of contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1245-1277, April.
    10. Gabriela Ciuperca, 2014. "Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(2), pages 349-374, May.
    11. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    12. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    13. Robert Tibshirani, 2011. "Regression shrinkage and selection via the lasso: a retrospective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 273-282, June.
    14. Philippe Aghion & Steven Durlauf (ed.), 2005. "Handbook of Economic Growth," Handbook of Economic Growth, Elsevier, edition 1, volume 1, number 1.
    15. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    16. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    17. Wei Lin & Jinchi Lv, 2013. "High-Dimensional Sparse Additive Hazards Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 247-264, March.
    18. 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.
    19. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
    20. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    21. Gabriela Ciuperca, 2014. "Erratum to: Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(4), pages 1231-1232, November.
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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," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1511-1543.
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    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. 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).
    18. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. 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".
    20. Yan, Hongqiang & Goodwin, Barry K. & Caner, Mehmet, 2023. "Investigating Integration and Exchange Rate Pass-Through in World Maize Markets Using Inferential LASSO Methods," 2023 Annual Meeting, July 23-25, Washington D.C. 335707, Agricultural and Applied Economics Association.
    21. 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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