D-Trace estimation of a precision matrix with eigenvalue control

Vahe Avagyan*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

The estimation of a precision matrix has an important role in several research fields. In high dimensional settings, one of the most prominent approaches to estimate the precision matrix is the Lasso norm penalized convex optimization. This framework guarantees the sparsity of the estimated precision matrix. However, it does not control the eigenspectrum of the obtained estimator. Moreover, Lasso penalization shrinks the largest eigenvalues of the estimated precision matrix. In this article, we focus on D-trace estimation methodology of a precision matrix. We propose imposing a negative trace penalization on the objective function of the D-trace approach, aimed to control the eigenvalues of the estimated precision matrix. Through extensive numerical analysis, using simulated and real datasets, we show the advantageous performance of our proposed methodology.

Original languageEnglish
Number of pages18
JournalCommunications in statistics: Simulation and computation
DOIs
Publication statusE-pub ahead of print - 12 Mar 2019

Keywords

  • D-trace
  • Gaussian graphical model
  • gene expression
  • Hannan-Quinn information criterion
  • trace penalization

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