We identify recurrent ingredients in the antithetic sampling literature leading to a unified sampling framework. We introduce a new class of antithetic schemes that includes the most used antithetic proposals. This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's $\tau$ and Spearman's $\rho$; iii)ranking in concordance order and iv) a central limit theorem that characterizes stochastic behavior of Monte Carlo estimators when the sample size tends to infinity. Finally, we provide applications to Monte Carlo integration and Markov Chain Monte Carlo Bayesian estimation.

翻译：我们确定了导致统一取样框架的抗遗传抽样文献中的经常性成分。我们引入了一种新的抗遗传计划类别,其中包括最常用的抗遗传提案。这一视角使得能够得出采样计划的新特性:(一) Kullback-Leiber 感知的最佳性;(二) 封闭式多变式Kendall的美元和Spearman的美元;(三) 调和顺序排序,以及(四) 在采样规模趋向无限时蒙特卡洛测量员的随机行为特征的中央界限。最后,我们向蒙特卡洛集成和Markov 链 蒙特卡洛·巴耶西亚估算提供了应用。