Negative Dependence in Sampling
Negative Dependence in Sampling
复制标题
抽样中的负相关性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Jonasson
中科院分区：
文献类型：
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作者：
P. Brändén;J. Jonasson
摘要：强瑞利性质是一种新的、鲁棒的负相关性质，它意味着负关联;事实上，它意味着在外场下封闭的条件负关联（CNA+）。 假设和是两个满足强瑞利性质的0 - 1随机变量族，令。我们表明，{Zi}的条件也是强瑞利，这原来是一个简单的后果的结果保多项式的稳定性Borcea和Brändén（发明。数学、177，2009，521-569）。这意味着许多重要的πps采样算法，包括Sampford采样和Pareto采样，都是CNA+。因此，基于这些样本的统计数据自动满足三角形阵列的中心极限定理的一个版本。
Abstract. The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that and are two families of 0‐1 random variables that satisfy the strong Rayleigh property and let . We show that {Zi} conditioned on is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea & Brändén (Invent. Math., 177, 2009, 521–569). This entails that a number of important πps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.