Parsimonious Model Averaging With a Diverging Number of Parameters
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参数维度增长下的简约模型平均
- 研究问题
- 当参数数量随样本增长时，如何通过模型平均权重选择获得含较多零系数的简约估计，并兼顾模型误设下的预测表现？
- 方法与思路
- 作者提出新的权重选择准则，分别分析候选集中存在正确模型及所有候选模型均误设的情形，推导相应渐近性质。
- 材料陈述的贡献
- 摘要称存在正确模型时可将权重集中于最小正确模型并得到系数渐近分布；全部误设时，预测损失与风险具有渐近最优性。
- 阅读关注点
- 应核对参数维度与候选模型规模的增长条件、权重约束和准则形式，以及最小正确模型定义与预测最优性的比较对象。
- 阅读边界
- 依据稿件版本未注明的 OpenAlex 索引摘要，不能判断刊本变化；摘要未说明完整渐近条件，最优性仅针对所述比较对象与损失。
原文摘要
Model averaging generally provides better predictions than model selection, but the existing model averaging methods cannot lead to parsimonious models. Parsimony is an especially important property when the number of parameters is large. To achieve a parsimonious model averaging coefficient estimator, we suggest a novel criterion for choosing weights. Asymptotic properties are derived in two practical scenarios: (i) one or more correct models exist in the candidate model set and (ii) all candidate models are misspecified. Under the former scenario, it is proved that our method can put the weight one to the smallest correct model and the resulting model averaging estimators of coefficients have many zeros and thus lead to a parsimonious model. The asymptotic distribution of the estimators is also provided. Under the latter scenario, prediction is mainly focused on and we prove that the proposed procedure is asymptotically optimal in the sense that its squared prediction loss and risk are asymptotically identical to those of the best-but infeasible-model averaging estimator. Numerical analysis shows the promise of the proposed procedure over existing model averaging and selection methods.