Testing Equivalence to Families of Multinomial Distributions with Application to the Independence Model

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. In order to make the bootstrap computationally feasible we introduce an efficient and consistent estimator of the boundary points. The asymptotic consistence and optimality of bootstrap based tests is proven.We apply proposed equivalence tests to the independence model of two-way contingency tables. The finite sample performance is studied by Monte Carlo simulation. Finally we apply tests to real data sets.The tests are initially implemented in VB.NET and available on GitHub, see github.com/TestingEquivalence/ApproximateIndependence. All simulations results in this paper are based on this VB.NET code.More recently, the tests are improved and implemented in R, see github.com/TestingEquivalence/EquivalenceProductFamilieR