Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $σ^2$ in the model $Z_{i,n}=σn^{-β}X_i+Y_i,i=1,\ldots,n,β>0$ with independent, stationary Gaussian processes $(X_i)_{i\in\mathbb{N}}$, $(Y_i)_{i\in\mathbb{N}}$, and $(X_i)_{i\in\mathbb{N}}$ exhibits possibly long-range dependence. In a second part, closed-form expressions for the asymptotic behavior of the corresponding Fisher information are derived. Our main finding is that depending on the behavior of the spectral densities at zero, the Fisher information has asymptotically two different scaling regimes, which are separated by a sharp phase transition. The most prominent example included in our analysis is the Fisher information for the scaling factor of a high-frequency sample of fractional Brownian motion under additive noise.
Maximum Fisher information in mixed state quantum systems
我们处理的最大化经典Fisher信息的量子系统依赖于一个未知的参数。这个问题已经由物理学家提出，他们定义了[Helstrom（1967）Phys. Lett. A 25 101-102]经典Fisher信息的量子对应物，已经发现其构成经典信息本身的上界[Braunstein和Caves（1994）Phys. Rev. Lett. 72 3439-3443]。然后，它成为统计学家的相关兴趣，他们研究了经典信息和量子信息之间的关系，并在二维纯态系统的特定情况下导出了相等的条件[Barndorff-Nielsen and Gill（2000）J. Phys. A 33 4481-4490]。在本文中，我们表明，即使在更一般的设置二维混合状态系统，这个条件成立。我们还推导出了可获得的最大Fisher信息的表达式及其与纯态可获得的最大Fisher信息的关系。
On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes
Samovar laboratory, Telecom SudParis, Institut Polytechnique de Paris（萨莫瓦尔实验室，电信巴黎理工学院，巴黎理工学院）；Taif University, College of Engineering, Dept. of Electrical Engineering（塔伊夫大学，工程学院，电气工程系）
A Fisher's exact test justification of the TF-IDF term-weighting scheme
School of Mathematical and Computational Sciences, University of Prince Edward Island（王子爱岛大学数学与计算科学学院）；Canadian Centre for Climate Change and Adaptation, University of Prince Edward Island（加拿大气候变化与适应中心，王子爱岛大学）；Faculty of Sustainable Design Engineering, University of Prince Edward Island（可持续设计工程学院，王子爱岛大学）
