Local asymptotic normality property for fractional Gaussian noise under high-frequency observations
高频观测下分数高斯噪声的局部渐近正态性
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…