The Annals of Statistics
- Ann. Statist.
- Volume 46, Number 5 (2018), 2045-2061.
Local asymptotic normality property for fractional Gaussian noise under high-frequency observations
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.
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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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