Electronic Journal of Statistics

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

Yuta Koike

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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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 1443-1522.

Dates
Received: September 2018
First available in Project Euclid: 16 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1555380049

Digital Object Identifier
doi:10.1214/19-EJS1553

Mathematical Reviews number (MathSciNet)
MR3939303

Zentralblatt MATH identifier
07056156

Subjects
Primary: 60F05: Central limit and other weak theorems 60H07: Stochastic calculus of variations and the Malliavin calculus 62H15: Hypothesis testing

Keywords
Bootstrap central limit theorem Chernozhukov-Chetverikov-Kato theory high-frequency data Malliavin calculus multiple testing

Rights
Creative Commons Attribution 4.0 International License.

Citation

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


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