We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving weighted--type distances between characteristic functions and are convenient from the computational point of view if the weight function is properly chosen. The asymptotic behavior of the tests under the null hypothesis is investigated, and numerical studies are conducted in order to examine the performance of the criteria in finite samples.

翻译：我们建议三项试验标准,其中每一项标准都分别适合于以多变量数据分别测试对称性、同质性和独立性的等同假设,所有数量都具有涉及特性功能之间加权类型距离的共同特征,如果正确选择加权函数,从计算角度来说是方便的。 对无效假设下试验的无症状行为进行了调查,并进行了数字研究,以审查有限样品中标准性能。