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。
英文摘要：
We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of classical Fisher information, which has been found to constitute an upper bound for classical information itself [Braunstein and Caves (1994) Phys. Rev. Lett. 72 3439-3443]. It has then become of relevant interest among statisticians, who investigated the relations between classical and quantum information and derived a condition for equality in the particular case of two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys. A 33 4481-4490]. In this paper we show that this condition holds even in the more general setting of two-dimensional mixed state systems. We also derive the expression of the maximum Fisher information achievable and its relation with that attainable in pure states.
On the maximum likelihood degree of linear mixed models with two variance components
本文推广了Gross等人[Electron. J. Stat.]中提出的单向随机效应模型的最大似然度和REML度的上界的结果。6（2012），pp. 993-1016]的方法推广到具有两个方差分量的正态线性混合模型的情况。然后，我们证明了Gross等人的论文中的猜想1的两个部分，它涉及单向随机效应模型的某种扩展，在相当温和的条件下是正确的。
Asymptotic Theory for Restricted Maximum Likelihood Estimators in Generalized Linear Mixed Models
School of Systems and Computing, University of New South Wales（新南威尔士大学系统计算学院）；UNSW Data Science Hub（新南威尔士大学数据科学中心）；School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）
