Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance

2018/06/13 by Yuta Koike, Koike, Yuta
Decision Sciences · Mathematics · #60F05 #60H07 #62H15 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1806.05077

openalex publication_date 2018/06/13 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Common risk factors in the returns on stocks and bonds
• Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications
• Asymptotic expansion of Skorohod integrals

Related

• Spectral norm bounds for high-dimensional realized covariance matrices and application to weak factor models
• High-dimensional Central Limit Theorems by Stein's Method in the Degenerate Case
• High-dimensional limit theorems for random vectors in ℓ_pⁿ-balls
• Multi-dimensional Gaussian fluctuations on the Poisson space
• High-dimensional Central Limit Theorems by Stein's Method