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Sparse precision matrix estimation with calibration

Author(s): Zhao, T; Liu, H

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Abstract: We propose a semiparametric procedure for estimating high dimensional sparse inverse covariance matrix. Our method, named ALICE, is applicable to the elliptical family. Computationally, we develop an efficient dual inexact iterative projection (D2P) algorithm based on the alternating direction method of multipliers (ADMM). Theoretically, we prove that the ALICE estimator achieves the parametric rate of convergence in both parameter estimation and model selection. Moreover, ALICE calibrates regularizations when estimating each column of the inverse covariance matrix. So it not only is asymptotically tuning free, but also achieves an improved finite sample performance. We present numerical simulations to support our theory, and a real data example to illustrate the effectiveness of the proposed estimator.
Publication Date: 2013
Citation: Zhao, Tuo, and Han Liu. "Sparse precision matrix estimation with calibration." In Advances in Neural Information Processing Systems 26, pp. 2274-2282. 2013.
ISSN: 1049-5258
Pages: 2274 - 2282
Type of Material: Conference Article
Journal/Proceeding Title: Advances in Neural Information Processing Systems
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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