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February 2021 Inference problem in generalized fractional Ornstein–Uhlenbeck processes with change-point
Sévérien Nkurunziza
Bernoulli 27(1): 107-134 (February 2021). DOI: 10.3150/20-BEJ1230

Abstract

In this paper, we study an inference problem in generalized fractional Ornstein–Uhlenbeck (O–U) processes with an unknown change-point when the drift parameter is suspected to satisfy some constraints. The constraint considered is very general and, the testing problem studied generalizes a very recent inference problem in generalized O–U processes. We derive the unrestricted estimator (UE) and the restricted estimator (RE) and we establish the asymptotic properties of the UE and RE. We also propose some shrinkage-type estimators (SEs) as well as a test for testing the constraint. Finally, we derive the asymptotic power of the proposed test and we study the relative risk dominance of the proposed estimators.

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Sévérien Nkurunziza. "Inference problem in generalized fractional Ornstein–Uhlenbeck processes with change-point." Bernoulli 27 (1) 107 - 134, February 2021. https://doi.org/10.3150/20-BEJ1230

Information

Received: 1 December 2019; Revised: 1 April 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282844
MathSciNet: MR4177363
Digital Object Identifier: 10.3150/20-BEJ1230

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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