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A0286
Title: Relative error-based model averaging Authors:  Xiaochao Xia - Chongqing University (China) [presenting]
Abstract: A relative error-based model averaging (REMA) approach is proposed to predict the positive response data under a set of multiplicative error models. To estimate the parameters in each candidate multiplicative model, we utilize a relative error-type loss as empirical objective function. Specifically, two commonly used losses: the least product relative error (LPRE) and the least absolute relative error (LARE) are considered, under which two model averaging estimators, REMA-LPRE and REMA-LARE, are proposed accordingly. The involved optimal weight vector, $\mathbf{w}$, is chosen by minimizing a jackknife version of the relative error loss over $\mathcal{H}_n=\{\mathbf{w}\in [0,1]^M, \sum_{m=1}^{M} w_m =1\}$, where $M$ denotes the number of candidate models. 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 infeasible but best model averaging estimator. Furthermore, we present an extension to relaxing the summation constraint in $\mathcal{H}_n$, in which the asymptotic optimality for the LPRE-based model averaging estimator is still established. Extensive simulations and empirical applications are conducted to demonstrate the usefulness of our approach.