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Lasso regression in sparse linear model with $$\varphi $$ φ -mixing errors

Author

Listed:
  • Ling Peng

    (Jiangxi University of Economics and Finance)

  • Yan Zhu

    (University of Shanghai for Science and Technology)

  • Wenxuan Zhong

    (Shanghai University of International Business and Economics)

Abstract

This paper investigates the Lasso method for sparse linear models with exponential $$\varphi $$ φ -mixing errors under a fixed design, where the number of covariates p is large, or even much larger than the sample size n. The non-asymptotic concentration inequalities for the estimation and prediction errors of the Lasso estimators are given when the errors follow the Gaussian distribution and the sub-exponential distribution, respectively. The prediction and variable selection performance of Lasso estimators are further illustrated through numerical simulations. Finally, the results of the empirical application show that the Index Tracking Fund based on the sparse selection of Lasso can closely track the trend of the target index, and thus provide some useful guidance for the investors.

Suggested Citation

  • Ling Peng & Yan Zhu & Wenxuan Zhong, 2023. "Lasso regression in sparse linear model with $$\varphi $$ φ -mixing errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 1-26, January.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:1:d:10.1007_s00184-022-00860-7
    DOI: 10.1007/s00184-022-00860-7
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    References listed on IDEAS

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    3. Hipp, Christian, 1979. "Convergence rates in the central limit theorem for stationary mixing sequences of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 560-578, December.
    4. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
    5. Fang Xie & Zhijie Xiao, 2018. "Square†Root LASSO for High†Dimensional Sparse Linear Systems with Weakly Dependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 212-238, March.
    6. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    7. 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.
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