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真实模型包含在候选集中时最小二乘模型平均的渐近最优性AI 解读

Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or on the assumption that there is no true model with fixed dimensions in the candidate set. The focus of this article is to overcome these difficulties by studying a class of least squares model averaging methods with nested candidate models, which includes Mallows model averaging (MMA) of Hansen (2007, Econometrica 75,…

风险价值与期望损失联合回归的最优模型平均AI 解读

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under…

从模型选择到模型平均：嵌套线性模型的比较AI 解读

Model selection (MS) and model averaging (MA) are two popular approaches when many candidate models exist. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former is more flexible, but a foundational issue is this: Does MA offer a substantial improvement over MS? Recently, seminal work by Peng and Yang (2022) has answered this question under nested models with linear orthonormal series expansion. In the current paper, we…