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Lasso for sparse linear regression with exponentially β-mixing errors

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  • Xie, Fang
  • Xu, Lihu
  • Yang, Youcai

Abstract

We prove two consistency theorems for the lasso estimators of sparse linear regression models with exponentiallyβ-mixing errors, in which the number of regressors p is large, even much larger than the sample size n.

Suggested Citation

  • Xie, Fang & Xu, Lihu & Yang, Youcai, 2017. "Lasso for sparse linear regression with exponentially β-mixing errors," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 64-70.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:64-70
    DOI: 10.1016/j.spl.2017.01.023
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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. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    3. Ren, Yunwen & Xiao, Zhiguo & Zhang, Xinsheng, 2013. "Two-step adaptive model selection for vector autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 349-364.
    4. Clifford Lam & Pedro Souza, 2014. "Regularization for Spatial Panel Time Series Using the Adaptive LASSO," STICERD - Econometrics Paper Series 578, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    6. 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.
    7. repec:cep:stiecm:/2014/578 is not listed on IDEAS
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    Cited by:

    1. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.

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