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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1534492828

Digital Object Identifier
doi:10.1214/17-AOS1611

Mathematical Reviews number (MathSciNet)
MR3845010

Zentralblatt MATH identifier
06964325

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1534492828


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