We propose a test of mutual independence between random vectors with arbitrary dimensions. Our approach is based on the $L_1-$distance between the joint density and the product of the marginal densities. We establish the asymptotic normal approximation of the corresponding statistic under the null hypothesis without assuming any regularity conditions. From a practical point of view, we perform numerical studies in order to assess the efficiency of our procedure and compare it to existing independence tests in the literature. For many examples investigated, the proposed test provides good performance compared with existing methods.

翻译：我们建议对任意尺寸的随机矢量之间相互独立进行测试,我们的方法以联合密度和边际密度产品之间的1美元距离为基础。我们根据无效假设确定相应的统计数据的无症状的正常近似值,而不假定任何正常条件。从实际的角度来看,我们进行数字研究,以便评估我们程序的效率,并将其与文献中现有的独立测试进行比较。对于所调查的许多例子,提议的测试提供了与现有方法相比的良好性能。