D-trace estimation of a precision matrix using adaptive Lasso penalties |
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Authors: | Vahe Avagyan Andrés M Alonso Francisco J Nogales |
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Institution: | 1.Department of Applied Mathematics, Computer Science and Statistics,Ghent University,Ghent,Belgium;2.Department of Statistics,Universidad Carlos III de Madrid,Getafe,Spain;3.Department of Statistics,Universidad Carlos III de Madrid,Leganes,Spain |
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Abstract: | The accurate estimation of a precision matrix plays a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the \(\ell _1\) norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimate for properly selected penalty parameters. However, the \(\ell _1\) norm penalization often fails to control the bias of obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed \(\ell _1\) norm penalized D-trace loss minimization method. They aim at reducing the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators. |
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