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：我们提出了三种检验准则，分别适用于多变量数据下对称性、同质性和独立性等价假设的检验。所有检验量均涉及特征函数间加权型距离的共同特征，且当权重函数选择适当时，在计算上具有便利性。本文研究了这些检验在零假设下的渐近行为，并通过数值模拟考察了各准则在有限样本中的性能表现。