Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series
Zhai, Percy S Kolar, Mladen Wu, Wei Biao
Zhai, Percy S
Kolar, Mladen
Wu, Wei Biao
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Statistics and Data Science
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Journal article
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English
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Abstract
For time series with long-range temporal dependence, inference for covariance and precision matrices is non-trivial. We propose a Berry-Esseen type Gaussian approximation result that gives a finite-sample bound for the Kolmogorov distance between the infinity norms of the estimation error of sample covariance matrix and the corresponding Gaussian approximation. The method utilizes martingale and m-dependent approximation and relies on constructing triadic blocks. We also establish a bootstrapping result with block sampling method, which preserves validity despite strong temporal dependence. Our results on covariance allow ultra-high-dimensional settings where the dimension of time series can grow sub-exponentially with sample size. Similar results can be built for precision matrix under low-dimensional settings. No assumption is required on the structure of covariance and precision matrices.
Citation
P.S. Zhai, M. Kolar, W.B. Wu, "Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series," IEEE Transactions on Information Theory, vol. 72, no. 06, pp. 1-1, 2026, https://doi.org/10.1109/tit.2026.3685246.
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IEEE Transactions on Information Theory
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46 Information and Computing Sciences, 4613 Theory Of Computation, 3 Good Health and Well Being
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IEEE