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October 2018 Local asymptotic normality property for fractional Gaussian noise under high-frequency observations
Alexandre Brouste, Masaaki Fukasawa
Ann. Statist. 46(5): 2045-2061 (October 2018). DOI: 10.1214/17-AOS1611

Abstract

Local Asymptotic Normality (LAN) property for fractional Gaussian noise under high-frequency observations is proved with nondiagonal rate matrices depending on the parameter to be estimated. In contrast to the LAN families in the literature, nondiagonal rate matrices are inevitable. As consequences of the LAN property, a maximum likelihood sequence of estimators is shown to be asymptotically efficient and the likelihood ratio test on the Hurst parameter is shown to be an asymptotically uniformly most powerful unbiased test for two-sided hypotheses.

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Alexandre Brouste. Masaaki Fukasawa. "Local asymptotic normality property for fractional Gaussian noise under high-frequency observations." Ann. Statist. 46 (5) 2045 - 2061, October 2018. https://doi.org/10.1214/17-AOS1611

Information

Received: 1 October 2016; Revised: 1 February 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964325
MathSciNet: MR3845010
Digital Object Identifier: 10.1214/17-AOS1611

Subjects:
Primary: 62F05 , 62F12

Keywords: fractional Brownian motion , high-frequency data , likelihood ratio test , Locally asymptotically normal families , maximum likelihood estimators

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 5 • October 2018
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