ESTIMATORS OF A LOCATION PARAMETER IN THE ABSOLUTELY CONTINUOUS CASE
ESTIMATORS OF A LOCATION PARAMETER IN THE ABSOLUTELY CONTINUOUS CASE
复制标题
绝对连续情况下位置参数的估计
DOI：
10.1214/aoms/1177700516
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发表时间：
1964
影响因子：
--
通讯作者：
R. H. Farrell
中科院分区：
文献类型：
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作者：
R. H. Farrell
0. 总结。在过去的十年中，有许多论文涉及位置参数的平移不变估计量的可接受性。 Blyth [2] 在正态或矩形分布随机变量的情况下处理顺序过程。如果 d 是估计值并且 0 是实际参数值，对于 Blyth，op。如上所述，损失通过 W(ld 01) 来测量，其中 W(.) 是 [0, oo) 上的非减函数。同年，Blackwell [1] 处理了离散随机变量仅取有限数量值的情况下的固定样本量问题。对于布莱克威尔，同上。如上所述，损耗通过 W(d 0) 来测量，其中 W(.) 假设是连续的并且从下面开始有界，但在其他方面是任意的。布莱克威尔表明，如果离散随机变量（可以是向量值）仅在整数格点上取值，并且如果存在唯一的极小极大平移不变估计量，那么它是可接受的。 Karlin [7] 和 Stein [11] 后来的论文讨论了 Pitman 平方误差估计量的可接受性。在审查这些结果时，我们发现如果损失满足
0. Summary. In the last decade there have been a number of papers dealing with the admissibility of translation invariant estimators of a location parameter. Blyth [2] treated sequential procedures in the case of normally or rectangularly distributed random variables. If d is estimated and 0 is the actual parameter value, for Blyth, op. cit., loss was measured by W(ld 01) where W(.) was a nondecreasing function on [0, oo). In the same year Blackwell [1] treated the fixed sample size problem in the case of discrete random variables taking only a finite number of values. For Blackwell, op. cit., loss was measured by W(d 0) where W(.) was assumed continuous and bounded from below but otherwise arbitrary. Blackwell showed that if the discrete random variables (which could be vector valued) took values only on the integer lattice points and if there was a unique minimax translation invariant estimator then it was admissible. Later papers by Karlin [7] and Stein [11] discuss the admissibility of Pitman's estimator for square error. In reviewing these results we discovered that if the loss satisfied
DOI：
10.1002/9781118231296.ch8
发表时间：
2018-11
期刊：
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics
影响因子：
--
作者：
Dr. Gergely Záruba
通讯作者：
Dr. Gergely Záruba