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D-trace estimation of a precision matrix using adaptive Lasso penalties

Author

Listed:
  • Vahe Avagyan

    (Ghent University
    Universidad Carlos III de Madrid)

  • Andrés M. Alonso

    (Universidad Carlos III de Madrid)

  • Francisco J. Nogales

    (Universidad Carlos III de Madrid)

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 $$\ell _1$$ ℓ 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 $$\ell _1$$ ℓ 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 $$\ell _1$$ ℓ 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.

Suggested Citation

  • Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2018. "D-trace estimation of a precision matrix using adaptive Lasso penalties," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 425-447, June.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:2:d:10.1007_s11634-016-0272-8
    DOI: 10.1007/s11634-016-0272-8
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    Cited by:

    1. Vahe Avagyan, 2022. "Precision matrix estimation using penalized Generalized Sylvester matrix equation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 950-967, December.
    2. Fang, Qian & Yu, Chen & Weiping, Zhang, 2020. "Regularized estimation of precision matrix for high-dimensional multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).

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