The Annals of Statistics

Local asymptotic normality property for fractional Gaussian noise under high-frequency observations

Alexandre Brouste and Masaaki Fukasawa

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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.

Article information

Ann. Statist., Volume 46, Number 5 (2018), 2045-2061.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F05: Asymptotic properties of tests 62F12: Asymptotic properties of estimators

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


Brouste, Alexandre; Fukasawa, Masaaki. Local asymptotic normality property for fractional Gaussian noise under high-frequency observations. Ann. Statist. 46 (2018), no. 5, 2045--2061. doi:10.1214/17-AOS1611.

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