Testing semiparametric model-equivalence hypotheses based on the characteristic function

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, homogeneity, and 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 behaviour of the tests under the null and alternative hypotheses is investigated. Numerical studies and a real-data application are conducted in order to examine the performance of the criteria in finite samples.