WIAS Preprint No. 2229, (2016)

Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix



Authors

  • Avanesov, Valeriy
  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658
  • Tabelow, Karsten
    ORCID: 0000-0003-1274-9951

2010 Mathematics Subject Classification

  • 62J07 62P10

Keywords

  • adaptive l1 penalty, precision matrix, high-dimensional statistics, sparsity, confidence intervals, functional connectivity

Abstract

In this paper we consider the adaptive l1-penalized estimators for the precision matrix in a finite-sample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments.

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