We study the notion of γ-negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to 1-negative dependence), but nevertheless it still ensures concentration of measure and allows to use large deviation bounds of Chernoff-Hoeffding- or Bernstein-type. We study random variables based on random points P. These random variables appear naturally in the analysis of the discrepancy of P or, equivalently, of a suitable worst-case integration error of the quasi-Monte Carlo cubature that uses the points in P as integration nodes. We introduce the correlation number, which is the smallest possible value of γ that ensures γ-negative dependence. We prove that the random variables of interest based on Latin hypercube sampling or on $(t,m,d)$-nets do, in general, not have a correlation number of 1, i.e., they are not negative orthant dependent.

我们研究了随机变量的γ负相关性的概念。这个概念是对负相关（对应于 1-负相关）概念的放宽，但它仍然确保了度量的集中，并允许使用 Chernoff-Hoeffding 或 Bernstein 类型的大偏差界限。我们研究基于随机点P 的随机变量。这些随机变量自然出现在P的差异的分析中，或者等效地，在使用P 中的点作为积分节点的准蒙特卡洛体积的合适的最坏情况积分误差的分析中出现。我们介绍了相关性数，这是最小的可能值γ，以确保γ- 负依赖。我们证明感兴趣的随机变量基于拉丁超立方抽样或$(吨,米,d)$-nets 通常不具有 1 的相关数，即它们不是负相关的。