We introduce the smooth total variation distance as a natural choice to establish equivalence. We propose asymptotic and bootstrap-based tests for which asymptotic optimality is shown. The finite sample performance is studied by simulations. Then we apply tests to real data sets. The tests are...

We introduce efficient tests for equivalence to families of multinomial distributions. Asymptotic distribution of the test statistic is derived and the local asymptotic optimality of proposed tests is shown.The finite sample performance of tests is improved by means of the parametric bootstrap....