Estimation of a sparse group of sparse vectors

Felix Abramovich, Vadim Grinshtein

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Jun 2013


FundersFunder number
Israel Science Foundation


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


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