Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance
Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance
复制标题
DOI：
10.1214/19-ejs1553
复制
发表时间：
2018-06
影响因子：
1.1
通讯作者：
Yuta Koike
中科院分区：
文献类型：
--
作者：
Yuta Koike
本文给出了多重Skorohod积分向量在维数可能发散到无穷大时属于随机凸多面体的概率的混合正态逼近。我们应用所发展的理论，建立了一个高维连续半鞅的实现协方差矩阵的渐近混合正态性，在一个高频率的观察，其中的维度可以远远大于样本容量。我们还提出了一个应用程序，这个结果来测试一个高维连续时间因子模型的剩余稀疏性。
This paper develops mixed-normal approximations for probabilities that vectors of multiple Skorohod integrals belong to random convex polytopes when the dimensions of the vectors possibly diverge to infinity. We apply the developed theory to establish the asymptotic mixed normality of the realized covariance matrix of a high-dimensional continuous semimartingale observed at a high-frequency, where the dimension can be much larger than the sample size. We also present an application of this result to testing the residual sparsity of a high-dimensional continuous-time factor model.