LOCAL ASYMPTOTIC NORMALITY PROPERTY FOR FRACTIONAL GAUSSIAN NOISE UNDER HIGH-FREQUENCY OBSERVATIONS

• 成果类型: Article
• 署名作者: Brouste, Alexandre; Fukasawa, Masaaki
• 署名单位: Le Mans Universite; University of Osaka
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1611
• 发表日期: 2018
• 页码: 2045-2061
• 关键词: lan property; parameter

摘要

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.