Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 1 (2019), 1443-1522.
Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance
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.
Electron. J. Statist., Volume 13, Number 1 (2019), 1443-1522.
Received: September 2018
First available in Project Euclid: 16 April 2019
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Koike, Yuta. Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance. Electron. J. Statist. 13 (2019), no. 1, 1443--1522. doi:10.1214/19-EJS1553. https://projecteuclid.org/euclid.ejs/1555380049