Consistent ordered sampling distributions : characterization and convergence
Consistent ordered sampling distributions : characterization and convergence
复制标题
一致的有序采样分布：表征和收敛
DOI：
10.1017/s0001867800023478
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发表时间：
1991
影响因子：
1.2
通讯作者：
P. Joyce
中科院分区：
文献类型：
--
作者：
P. Donnelly;P. Joyce
本文研究的是从总体中抽样的模型，其中存在类型集合的全序，但只有实际出现在样本中的类型的相对序是已知的。不同样本量之间的一致性需要限制了可能的模型，这里称为“一致有序抽样分布”。我们给出的条件下，弱收敛的人口分布意味着收敛的抽样分布，反之亦然，人口收敛可以推断出收敛的抽样分布。一个中心结果展示了一个“有序采样函数”的集合，其中没有一个是连续的，它将某个类中的测量分开。更一般地说，我们的特点是所有一致的有序抽样分布，证明了在这种情况下的德菲内蒂定理的模拟。这些结果适用于遗传学中的一个未解决的问题，它表明，平衡年龄有序的人口等位基因频率的广泛的一类可交换的生殖模型收敛弱，人口规模变得很大，所谓的GEM分布。这提供了一种替代的表征，它比金曼（1977）的泊松-狄利克雷分布的表征更有信息量，而且往往更方便。
This paper is concerned with models for sampling from populations in which there exists a total order on the collection of types, but only the relative ordering of types which actually appear in the sample is known. The need for consistency between different sample sizes limits the possible models to what are here called 'consistent ordered sampling distributions'. We give conditions under which weak convergence of population distributions implies convergence of sampling distributions and conversely those under which population convergence may be inferred from convergence of sampling distributions. A central result exhibits a collection of 'ordered sampling functions', none of which is continuous, which separates measures in a certain class. More generally, we characterize all consistent ordered sampling distributions, proving an analogue of de Finetti's theorem in this context. These results are applied to an unsolved problem in genetics where it is shown that equilibrium age-ordered population allele frequencies for a wide class of exchangeable reproductive models converge weakly, as the population size becomes large, to the so-called GEM distribution. This provides an alternative characterization which is more informative and often more convenient than Kingman's (1977) characterization in terms of the Poisson-Dirichlet distribution.