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Shrinking characteristics of precision matrix estimators

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  • Aaron J Molstad
  • Adam J Rothman

Abstract

SummaryWe propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an $L_1$ penalty on a linear or affine function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and propose an alternating direction method of multipliers algorithm for their computation. Our simulation studies show that our estimators can perform better than competitors when they are used to fit predictive models. In particular, we illustrate cases where our precision matrix estimators perform worse at estimating the population precision matrix but better at prediction.

Suggested Citation

  • Aaron J Molstad & Adam J Rothman, 2018. "Shrinking characteristics of precision matrix estimators," Biometrika, Biometrika Trust, vol. 105(3), pages 563-574.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:563-574.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy023
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    References listed on IDEAS

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    Cited by:

    1. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).

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