High-dimensional inference for Model Averaging estimators

Lise Léonard (), Eugen Pircalabelu () and Rainer von Sachs ()
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Lise Léonard: Université catholique de Louvain, LIDAM/ISBA, Belgium
Eugen Pircalabelu: Université catholique de Louvain, LIDAM/ISBA, Belgium
Rainer von Sachs: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2025014, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Debiased Lasso; High-Dimensional Inference; Model Averaging; Prediction Risk (search for similar items in EconPapers)
Pages: 28
Date: 2025-06-11
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