Elimination of Randomization in Certain Problems of Statistics and of the Theory of Games.
Elimination of Randomization in Certain Problems of Statistics and of the Theory of Games.
复制标题
消除统计和博弈论某些问题中的随机性。
DOI：
10.1073/pnas.36.4.256
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发表时间：
1950
影响因子：
11.1
通讯作者：
Jacob Wolfowitz
中科院分区：
文献类型：
--
作者：
A. Dvoretzky;Abraham Wald;Jacob Wolfowitz
1. 本文的主要目的是表明混合策略可以从基于连续分布函数的随机变量观察的统计决策规则中消除，也可以从类似结构的博弈中消除。在叙述了第2章的一般测量理论结果之后。我们用3来推导。和4。关于游戏的一些结果。在5。和6。我们给出了决策问题的一些结果。我们的方法所产生的结果比这里所呈现的要普遍得多（特别是它们可以应用于所谓的顺序游戏）。本文选择的结果是出于我们对统计问题的兴趣。关于这一课题的证明和更完整的研究将在其他地方发表。2. 设{x} = x是任意空间，{SI = 3是x子集的Borel域。设Mk(S) (k = 1,2，…， p)是有限个为所有S e S定义的实值、有界和数加性集合函数。在引言中提到的基本测度理论结果如下：定理1。设flj(x) （j = 1,2，…）， n)是满足的实非负3可测函数
1. The main aim of this note is to show that mixed strategies may be eliminated from statistical decision rules based on the observation of random variables with continuous distribution functions, and from games of a similar structure. After stating a general measure-theoretic result in 2. we deduce in 3. and 4. some results on games. In 5. and 6. we give some results on decision problems. Our methods lead to considerably more general results than those presented here (in particular they can be applied to what may be termed sequential games). The selection of results presented here was motivated by our interest in statistical problems. Proofs and a more complete study of the subject will be published elsewhere. 2. Let {x} = X be any space and {SI = 3 a Borel field of subsets of X. Let Mk(S) (k = 1, 2, ..., p) be a finite number of real-valued, bounded and countably additive set functions defined for all S e S. The fundamental measure theoretic result mentioned in the introduction is the following: THEOREM 1. Let flj(x) (j = 1, 2, .. ., n) be real non-negative 3-measurable functions satisfying