Sparse precision matrix estimation with calibration

Tuo Zhao, Han Liu

Research output: Contribution to journalConference article

Abstract

We propose a semiparametric method for estimating sparse precision matrix of high dimensional elliptical distribution. The proposed method calibrates regularizations when estimating each column of the precision matrix. Thus it not only is asymptotically tuning free, but also achieves an improved finite sample performance. Theoretically, we prove that the proposed method achieves the parametric rates of convergence in both parameter estimation and model selection. We present numerical results on both simulated and real datasets to support our theory and illustrate the effectiveness of the proposed estimator.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
StatePublished - Jan 1 2013
Event27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States
Duration: Dec 5 2013Dec 10 2013

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Calibration
Parameter estimation
Tuning

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

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Sparse precision matrix estimation with calibration. / Zhao, Tuo; Liu, Han.

In: Advances in Neural Information Processing Systems, 01.01.2013.

Research output: Contribution to journalConference article

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AB - We propose a semiparametric method for estimating sparse precision matrix of high dimensional elliptical distribution. The proposed method calibrates regularizations when estimating each column of the precision matrix. Thus it not only is asymptotically tuning free, but also achieves an improved finite sample performance. Theoretically, we prove that the proposed method achieves the parametric rates of convergence in both parameter estimation and model selection. We present numerical results on both simulated and real datasets to support our theory and illustrate the effectiveness of the proposed estimator.

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