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Confidence intervals for sparse precision matrix estimation via Lasso penalized D-trace loss

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  • Huang Xudong
  • Li Mengmeng

Abstract

This article aims at establishing the confidence intervals for individual parameters of high-dimensional sparse precision matrix. Benefit from a precision matrix estimator which is defined as the minimizer of the Lasso penalized D-trace loss under a positive-definiteness constraint, we modify the KKT condition of the optimization problem to obtain a de-sparsified estimator. We analyze the asymptotic properties of the estimator under some regularity conditions and establish the asymptotic normality and confidence intervals for the case of sub-Gaussian observations. Numerical results show the performance of the proposed method.

Suggested Citation

  • Huang Xudong & Li Mengmeng, 2017. "Confidence intervals for sparse precision matrix estimation via Lasso penalized D-trace loss," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(24), pages 12299-12316, December.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:24:p:12299-12316
    DOI: 10.1080/03610926.2017.1295074
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