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2019 Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations
Daisuke Kurisu
Electron. J. Statist. 13(2): 2521-2565 (2019). DOI: 10.1214/19-EJS1584

Abstract

This study examines a nonparametric inference on a stationary Lévy-driven Ornstein-Uhlenbeck (OU) process $X=(X_{t})_{t\geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the Lévy measure of the Lévy-driven OU process $X$ under macroscopic observations. We also derive, for the estimator, multivariate central limit theorems over a finite number of design points, and high-dimensional central limit theorems in the case wherein the number of design points increases with an increase in the sample size. Built on these asymptotic results, we develop methods to construct confidence bands for the Lévy measure and propose a practical method for bandwidth selection.

Citation

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Daisuke Kurisu. "Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations." Electron. J. Statist. 13 (2) 2521 - 2565, 2019. https://doi.org/10.1214/19-EJS1584

Information

Received: 1 May 2018; Published: 2019
First available in Project Euclid: 25 July 2019

zbMATH: 1426.62244
MathSciNet: MR3984260
Digital Object Identifier: 10.1214/19-EJS1584

Subjects:
Primary: 60F05, 62G15

JOURNAL ARTICLE
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Vol.13 • No. 2 • 2019
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