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High-dimensional inference for Model Averaging estimators

Author

Listed:
  • Léonard, Lise

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

  • Pircalabelu, Eugen

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

  • von Sachs, Rainer

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

Abstract

Selection methods for high-dimensional models are well developed, but they do not take into account the choice of the model, which leads to an underestimated variance. We propose a procedure for high-dimensional model averaging that allows inference even when the number of predictors is greater than the sample size. The proposed estimator is constructed from the debiased Lasso and the weights are chosen to reduce the prediction risk associated with them. We derive the asymptotic distribution of the estimator within a high-dimensional framework and offer guarantees for the minimal loss prediction obtained from the weights. With this, in contrast to existing approaches, our proposed method combines the advantages of model averaging with the possibility of inference based on asymptotic normality. In a simulation study and on a real, high-dimensional dataset, the estimator shows a smaller prediction risk than its competitors.

Suggested Citation

  • Léonard, Lise & Pircalabelu, Eugen & von Sachs, Rainer, 2025. "High-dimensional inference for Model Averaging estimators," LIDAM Discussion Papers ISBA 2025014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2025014
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    References listed on IDEAS

    as
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