Estimation of a sparse group of sparse vectors

Felix Abramovich, Vadim Grinshtein

Research output: Contribution to journalArticlepeer-review

Abstract

We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed as maximum a posteriori estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. A simulation study demonstrates the efficiency of the proposed approach, which successfully competes with the sparse group lasso estimator.

Original languageEnglish
Pages (from-to)355-370
Number of pages16
JournalBiometrika
Volume100
Issue number2
DOIs
StatePublished - Jun 2013

Keywords

  • Adaptive minimaxity
  • Complexity penalty
  • Maximum a posteriori rule
  • Sparsity
  • Thresholding

Fingerprint

Dive into the research topics of 'Estimation of a sparse group of sparse vectors'. Together they form a unique fingerprint.

Cite this