Sharpening Button's Needle
Sharpening Button's Needle
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磨纽扣针
DOI：
10.1080/00031305.1975.10477404
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
M. J. Wichura
中科院分区：
文献类型：
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作者：
M. Perlman;M. J. Wichura
著名的布丰针实验及其变化，提供了经验估计值的ir，继续产生有趣的和教育的应用统计理论。读者可以在[6，7，9，10，11，13，14，16，17]中找到对这个问题的历史发展以及最近的贡献的深入讨论。在本文第2节中回顾了布冯的原始实验之后，我们在第3节和第4节中继续介绍了两种变化的实验，其中统计理论被用来“锐化”布冯的针，通过获得-r的估计值，大大降低了抽样方差。我们关注的是（i）设计实验以提高估计器的效率（即，减少它们的方差）和（ii）以Rao-Blackwell-Lehmann-Scheffe定理[4，12]、Cramer-Rao下界[15]和条件性原则为幌子，应用充分性和完整性、效率和辅助性的概念[1，2，3，5]，以获得尽可能充分利用可用统计信息的替代估计量。
The famous needle experiment of Buffon and its variations, which provide empirical estimates of the value of ir, continue to yield amusing and educational applications of statistical theory. The reader will find thorough discussion of the historical development of this problem as well as recent contributions in [6, 7, 9, 10, 11, 13, 14, 16, 17]. After reviewing Buffon's original experiment in Section 2 of this article, we go on in Sections 3 and 4 to present two variations of the experiinent in which statistical theory is utilized to "sharpen" Buffon's needle by obtaining estimators for -r with dramatically reduced sampling variance. Our concern has been to (i) design the experiments to increase the efficiency of the estimators (i.e., reduce their variances) and (ii) apply the concepts of sufficiency and completeness, efficiency, and ancillarity, in the guise of the Rao-Blackwell-Lehmann-Scheffe theorems [4, 12], the Cramer-Rao lower bound [15], and the principle of conditionality [1, 2, 3, 5], to obtain alternate estimators which utilize the available statistical information as fully as possible.