A Scalable Frequentist Model Averaging Method
A Scalable Frequentist Model Averaging Method
复制标题
一种可扩展的频率模型平均方法
DOI：
10.1080/07350015.2022.2116442
复制
发表时间：
2022
影响因子：
3
通讯作者：
Liang, Hua
中科院分区：
文献类型：
--
作者：
Zhu, Rong;Wang, Haiying;Zhang, Xinyu;Liang, Hua
频率模型平均是处理模型不确定性的一种有效方法。然而，即使预测向量p的维数适中，计算平均权重也是极其困难的，因为我们可能有候选模型。候选模型集的指数大小使得难以估计所有候选模型，并且在计算权重时带来额外的数值误差。本文提出了一种可扩展的频率模型平均方法，这是统计和计算效率，克服这个问题，通过转换原始模型使用奇异值分解。该方法使我们能够找到最佳的权重，通过考虑至多p个候选模型。证明了可伸缩模型平均估计的最小损失渐近等于传统模型平均估计的最小损失。我们应用Mallow和Jackknife准则的可扩展模型平均估计，并证明他们是渐近最优估计。我们进一步扩展的方法，高维的情况下（即）。数值研究表明，所提出的方法在统计效率和计算成本方面的优越性。
Frequentist model averaging is an effective technique to handle model uncertainty. However, calculation of the weights for averaging is extremely difficult, if not impossible, even when the dimension of the predictor vector,p, is moderate, because we may havecandidate models. The exponential size of the candidate model set makes it difficult to estimate all candidate models, and brings additional numeric errors when calculating the weights. This article proposes a scalable frequentist model averaging method, which is statistically and computationally efficient, to overcome this problem by transforming the original model using the singular value decomposition. The method enables us to find the optimal weights by considering at mostpcandidate models. We prove that the minimum loss of the scalable model averaging estimator is asymptotically equal to that of the traditional model averaging estimator. We apply the Mallows and Jackknife criteria to the scalable model averaging estimator and prove that they are asymptotically optimal estimators. We further extend the method to the high-dimensional case (i.e.,). Numerical studies illustrate the superiority of the proposed method in terms of both statistical efficiency and computational cost.
用于估计响应的回归参数的共线性和最优限制
影响因子：
2.5
作者：
Sung H. Park
通讯作者：
Sung H. Park