We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic incarnations of these estimators with a class of generalized U-statistics, and thus establish their unbiasedness, consistency, and asymptotic normality. Moreover, we show that they obtain the minimum possible variance amongst a broad class of estimators; and we investigate their computational cost and delineate the settings in which they are most efficient. We exemplify the merger of these estimators with other well-known Monte Carlo estimators so as to better adapt the latter to the target's independence structure and improve their performance. We do this via three simple mergers: one with importance sampling, another with importance sampling squared, and a final one with pseudo-marginal Metropolis-Hasting. In all cases, we show that the resulting estimators are well-founded and achieve lower variances than their standard counterparts. Lastly, we illustrate the various variance reductions through several examples.

翻译：我们引入了一组蒙特卡洛测算员,目的是通过利用目标的独立结构,克服与标准测算员经常观察到的维度差异的迅速增长。我们确定这些测算员的最基本属性,具有普遍U-统计学的类别,从而确立其公正性、一致性和无症状的正常性。此外,我们表明,他们获得的分布在广泛的测算员类别之间可能存在的最低差异;我们调查其计算成本,并划定其效率最高的环境。我们将这些测算员与其他著名的蒙特卡洛测算员合并,以便更好地使后者适应目标的独立结构并改善其绩效。我们通过三个简单合并来做到这一点:一个是重要取样,另一个是重要取样方位,最后一个是伪边际大都会测算员。我们通过几个例子来说明由此产生的测算员的根据和差差差。最后,我们通过几个例子来说明各种差异的缩小。