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Relative error model average for multiplicative models
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DOI：10.1007/s11222-025-10773-w.png)
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Abstract
En 中文
We propose a relative error model averaging (REMA) approach to predict positive response values under a set of multiplicative error models. To estimate the parameters in each candidate multiplicative model, we utilize a relative error loss as the empirical objective function. Specifically, we consider two commonly used loss functions: the least product relative error (LPRE) and the least absolute relative error (LARE), under which two model averaging estimators, REMA-LPRE and REMA-LARE, are proposed accordingly. The optimal weight vector is chosen by minimizing a jackknife version of the relative error loss. Theoretically, it is shown that under some technical conditions, our proposed model averaging estimators enjoy asymptotic optimality under the two losses, respectively, in the sense that its loss defined by a final prediction error (FPE) is asymptotically identical to that of the best yet infeasible model averaging estimator. Furthermore, we propose a model-based screening approach to deal with the high-dimensional data setting when the number of candidate models are extremely large, and then present an extension to relax the sum-to-one constraint. Extensive simulations and empirical applications are conducted to demonstrate the practical performance of our approach.
Keywords:
Asymptotic optimality
Relative error loss
Jackknife
High-dimensional model averaging
Prediction error
Journal
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1.6
Papers:
200
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0