Ultrahigh dimensional precision matrix estimation via refitted cross validation

Luheng Wang, Zhao Chen, Christina Dan Wang and Runze Li

Journal of Econometrics, 2020, vol. 215, issue 1, 118-130

Abstract: This paper develops a new estimation procedure for ultrahigh dimensional sparse precision matrix, the inverse of covariance matrix. Regularization methods have been proposed for sparse precision matrix estimation, but they may not perform well with ultrahigh dimensional data due to the spurious correlation. We propose a refitted cross validation (RCV) method for sparse precision matrix estimation based on its Cholesky decomposition, which does not require the Gaussian assumption. The proposed RCV procedure can be easily implemented with existing software for ultrahigh dimensional linear regression. We establish the consistency of the proposed RCV estimation and show that the rate of convergence of the RCV estimation without assuming banded structure is the same as that of those assuming the banded structure in Bickel and Levina (2008b). Monte Carlo studies were conducted to access the finite sample performance of the RCV estimation. Our numerical comparison shows that the RCV estimation outperforms the existing ones in various scenarios. We further apply the RCV estimation for an empirical analysis of asset allocation.

Keywords: Covariance matrix estimation; Precision matrix; Refitted cross validation; Sample splitting; Spurious correlation (search for similar items in EconPapers)
JEL-codes: C13 C51 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:215:y:2020:i:1:p:118-130

DOI: 10.1016/j.jeconom.2019.08.004

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