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Confidence regions for entries of a large precision matrix

Jinyuan Chang, Yumou Qiu, Qiwei Yao and Tao Zou

Journal of Econometrics, 2018, vol. 206, issue 1, 57-82

Abstract: We consider the statistical inference for high-dimensional precision matrices. Specifically, we propose a data-driven procedure for constructing a class of simultaneous confidence regions for a subset of the entries of a large precision matrix. The confidence regions can be applied to test for specific structures of a precision matrix, and to recover its nonzero components. We first construct an estimator for the precision matrix via penalized node-wise regression. We then develop the Gaussian approximation to approximate the distribution of the maximum difference between the estimated and the true precision coefficients.A computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure. The theoretical justification is established under the setting which allows temporal dependence among observations. Therefore the proposed procedure is applicable to both independent and identically distributed data and time series data. Numerical results with both simulated and real data confirm the good performance of the proposed method.

Keywords: Bias correction; Dependent data; High dimensionality; Kernel estimation; Parametric bootstrap; Precision matrix (search for similar items in EconPapers)
JEL-codes: C12 C13 C15 (search for similar items in EconPapers)
Date: 2018
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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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