On Non-Regular Estimation. I. Variance Bounds for Estimators of Location Parameters
On Non-Regular Estimation. I. Variance Bounds for Estimators of Location Parameters
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关于非常规估计。
DOI：
10.1080/01621459.1969.10501036
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发表时间：
1969
影响因子：
3.7
通讯作者：
P. Mundle
中科院分区：
文献类型：
--
作者：
W. Blischke;A. J. Truelove;P. Mundle
摘要极大似然估计和其他BAN估计在估计满足特定正则性条件的概率分布参数时具有一定的最优渐近性质。非正规估计的主题涉及这些条件不成立的问题。在许多这样的问题中，经典的无偏估计量的方差下界，如Cramer-Rao界，导致平凡的结果V（t）≥ 0，其中t是任何无偏估计量。在非正则情况下的应用程序中的一些替代的界限已经推导出来。在本文中，这类以前的结果进行了审查，并给出了一个额外的界限。感兴趣的具体应用涉及位置参数的估计。指数，均匀和皮尔逊III型分布的界限的应用进行了研究。
Abstract Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramer-Rao bound, lead to the trivial result V(t) ≧0, where t is any unbiased estimator. A number of alternative bounds for application in the non-regular case have been derived. In this paper previous results of this type are reviewed and an additional bound is given. The specific applications of interest involve estimation of a location parameter. Applications of the bounds to the exponential, uniform and Pearson Type III distributions are investigated.