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High-dimensional inference for linear model with correlated errors

Author

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  • Panxu Yuan

    (University of Science and Technology of China)

  • Xiao Guo

    (University of Science and Technology of China)

Abstract

Temporally correlated error process is commonly encountered in practice and poses significant challenges in high-dimensional statistical analysis. This paper conducts low-dimensional inference for high-dimensional linear models with stationary errors. We adopt the framework of functional dependence measure for adequate accommodation of the error correlation. A new desparsifying Lasso based testing procedure is developed by incorporating a banded estimator of the error autocovariance matrix. Asymptotic normality of the proposed estimator is established by demonstrating the consistency of the banded autocovariance matrix estimator. The result indicates how the range of p is substantially narrower if the moment condition of error weakens or the dependence becomes stronger. We further develop a data-driven choice of the banding parameter. The simulation studies illustrate the satisfactory finite-sample performance of our proposed procedure, and a real data example is also presented for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00820-7
    DOI: 10.1007/s00184-021-00820-7
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    References listed on IDEAS

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    Cited by:

    1. Xiaorui Zhu & Yichen Qin & Peng Wang, 2023. "Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models," Papers 2307.07574, arXiv.org.

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