Statistical Information and Properties of Sufficiency
Statistical Information and Properties of Sufficiency
复制标题
统计信息和充分性的性质
DOI：
--
复制
发表时间：
1936
期刊：
影响因子：
--
通讯作者：
M. Bartlett
中科院分区：
文献类型：
--
作者：
M. Bartlett
在Fisher提出的统计估计理论中，一个基本特征是统计信息的概念，对于正态分布的估计定义为其抽样方差的倒数，更一般地定义为∂L/∂θ的方差，其中L是与我们对参数θ的估计相对应的似然函数的对数。期望值(∂L/∂θ)为零，这样我们可以写成I=E(∂L/∂θ)2。(1)如果∂L/∂θ对应于我们估计所基于的n个独立观测的原始样本，则其方差将是每个观测信息的n倍，因为∂L/∂θ是n个相似分量的和，并且(1)将给出我们样本中的信息。
In the theory of statistical estimation put forward by Fisher, an essential feature is the concept of statistical information, defined for estimates normally distributed as the reciprocal of their sampling variance, and more generally by the variance of ∂L/∂θ, where L is the logarithm of the likelihood function corresponding to our estimate of a parameterθ. The expected value (∂L/∂θ) is zero, so that we may write I = E(∂L/∂θ)2. (1) If ∂L/∂θ corresponds instead to the original sample of n independent observations from which our estimate was derived, its variance will be n times the information per observation, since ∂L/∂θ is then the sum of n similar components, and (1) will give the information in our sample.