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The generalized equivalence of regularization and min–max robustification in linear mixed models

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Listed:
  • Jan Pablo Burgard

    (Trier University)

  • Joscha Krause

    (Trier University)

  • Dennis Kreber

    (Trier University)

  • Domingo Morales

    (University Miguel Hernández de Elche)

Abstract

The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

Suggested Citation

  • Jan Pablo Burgard & Joscha Krause & Dennis Kreber & Domingo Morales, 2021. "The generalized equivalence of regularization and min–max robustification in linear mixed models," Statistical Papers, Springer, vol. 62(6), pages 2857-2883, December.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01214-z
    DOI: 10.1007/s00362-020-01214-z
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    References listed on IDEAS

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