LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE
LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE
复制标题
双指数分布情况下与订单统计和相关估计量相关的信息丢失
DOI：
10.1111/j.1467-842x.1990.tb01024.x
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
K. Takeuchi
中科院分区：
文献类型：
--
作者：
M. Akahira;K. Takeuchi
Fisher（1934）从他的基本论文（1922）开始，讨论了双指数（双侧指数）分布的位置参数的估计，作为非正则估计的一个典型例子。他证明了最大似然估计（MLE），在这种情况下等于样本中位数，与常规情况下的常数阶相比，具有阶\（\sqrt{n}\）的信息的渐近损失。设I和IT分别为单个观测值和统计量T中的Fisher信息量。那么当n → ∞时nI·IT的值，即limn→∞（nI-IT）称为与T有关的信息损失，当n → ∞时它的渐近值称为信息的渐近损失（例如参见Rao（1961））。
Fisher (1934), starting from his fundamental paper (1922), discussed estimators of the location parameter of a double exponential (two-sided exponential) distribution as a typical example of non-regular estimation. He showed that the maximum likelihood estimator (MLE), which is equal to the sample median in this case, has asymptotic loss of information of order \(\sqrt{n}\), as compared to constant order in regular cases. Let I and IT be the amounts of Fisher information in a single observation and that in a statistic T, respectively. Then the value of nI•IT as n → ∞, i.e. limn→∞ (nI — IT) is called the loss of information associated with T and its asymptotic value as n → ∞ is called the asymptotic loss of information (see, e.g. Rao (1961)).