Confidence regions for entries of a large precision matrix

Chang, Jinyuan, Qiu, Yumou, Yao, Qiwei ORCID: 0000-0003-2065-8486 and Zou, Tao (2018) Confidence regions for entries of a large precision matrix. Journal of Econometrics, 206 (1). pp. 57-82. ISSN 0304-4076

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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.

Item Type:	Article
Official URL:	https://www.journals.elsevier.com/journal-of-econo...
Additional Information:	© 2018 the Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
JEL classification:	C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C12 - Hypothesis Testing C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C15 - Statistical Simulation Methods; Monte Carlo Methods; Bootstrap Methods
Date Deposited:	18 Apr 2018 08:44
Last Modified:	11 Dec 2024 21:36
Projects:	JBK1802069, JBK171121, 11501462
Funders:	ANU Allocation Scheme, Fundamental Research Funds for the Central Universities, National Natural Science Foundation of China, Engineering and Physical Sciences Research Council
URI:	http://eprints.lse.ac.uk/id/eprint/87513

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