Zhu Rong, Zhang Xinyu, Ma Yanyuan, Zou Guohua
School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Econom J. 2020 Sep 29;24(1):177-197. doi: 10.1093/ectj/utaa030. eCollection 2021 Jan.
In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance estimators. Finally, we conduct numerical simulations and a case study on Chinese airport network structure data to demonstrate the usefulness of the proposed approaches.
在本文中，我们开发了一种模型平均方法来估计高维协方差矩阵，其中候选模型由不同阶数的多项式函数构建。我们提出了一种马洛斯型模型平均准则，并通过最小化该准则来选择权重，该准则是样本内期望平方误差加上一个常数的无偏估计量。然后，我们证明了所得模型平均协方差估计量的渐近最优性。最后，我们对中国机场网络结构数据进行了数值模拟和案例研究，以证明所提出方法的有效性。
