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Square†Root LASSO for High†Dimensional Sparse Linear Systems with Weakly Dependent Errors

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  • Fang Xie
  • Zhijie Xiao

Abstract

We study the square†root LASSO method for high†dimensional sparse linear models with weakly dependent errors. The asymptotic and non†asymptotic bounds for the estimation errors are derived. Our results cover a wide range of weakly dependent errors, including α†mixing, Ï â€ mixing, ϕ†mixing, and m†dependent types. Numerical simulations are conducted to show the consistency property of square†root LASSO. An empirical application to financial data highlights the importance of the results and method.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:2:p:212-238
    DOI: 10.1111/jtsa.12278
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    Cited by:

    1. 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.
    2. Panxu Yuan & Xiao Guo, 2022. "High-dimensional inference for linear model with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 21-52, January.

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