On tests of symmetry, marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum φ-divergence estimator with constraints

摘要

The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221-237], is employed to obtain estimates of the cell frequencies of an I x I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ_2 for estimation and the best function φ_1 for testing.