High-dimensional inference for linear model with correlated errors

Panxu Yuan () and Xiao Guo ()
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Panxu Yuan: University of Science and Technology of China
Xiao Guo: University of Science and Technology of China

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 1, No 2, 52 pages

Abstract: 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.

Keywords: Correlated errors; Desparsifying Lasso; Functional dependence measure; High-dimensional inference; Stationary time series (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-021-00820-7

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