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Unbalanced distributed estimation and inference for precision matrices

Author

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  • Nezakati, Ensiyeh

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Pircalabelu, Eugen

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

This paper studies the estimation of Gaussian graphical models in the unbalanced distributed framework. Unbalanced distributing is an effective approach when the available machines are of different powers or when the existing dataset comes from different resources with different sizes and can not be aggregated in one single computer. In this paper, we propose a new aggregated estimator of the precision matrix and justify such an approach by both theoretical and practical arguments. The limit distribution and consistency of this estimator are investigated. Furthermore, a procedure for performing statistical inference is proposed. On the practical side, a simulation study and real data examples are illustrated. We show that the performance of the distributed estimator is similar to that of the non-distributed estimator using the full data.

Suggested Citation

  • Nezakati, Ensiyeh & Pircalabelu, Eugen, 2021. "Unbalanced distributed estimation and inference for precision matrices," LIDAM Discussion Papers ISBA 2021031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021031
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    References listed on IDEAS

    as
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    2. Tore Schweder & Nils Lid Hjort, 2002. "Confidence and Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(2), pages 309-332, June.
    3. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    4. Tang, Lu & Zhou, Ling & Song, Peter X.-K., 2020. "Distributed simultaneous inference in generalized linear models via confidence distribution," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    5. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    6. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
    7. Xie, Minge & Singh, Kesar & Strawderman, William E., 2011. "Confidence Distributions and a Unifying Framework for Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 320-333.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Gaussian graphical models ; Precision matrix ; Lasso penalization ; Unbalanced distributed setting ; De-biased estimator ; Confidence distribution;
    All these keywords.

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