Title: On some characterizations of, and multidimensional criteria for testing, homogeneity, symmetry and independence
Authors: Feifei Chen - Beijing Normal University (China) [presenting]
Simos Meintanis - University of Athens (Greece)
Lixing Zhu - Hong Kong Baptist University (Hong Kong)
Abstract: Three new characterizations and corresponding distance-based weighted test criteria for the two-sample problem, and for testing symmetry and independence with multivariate data are proposed. All quantities have the common feature of involving characteristic functions, and it is seen that these quantities are intimately related to some earlier methods, thereby generalizing these methods. The connection rests on a special choice of the weight function involved. The new quantities however unlike their predecessors require no moment condition. Equivalent expressions of the distances in terms of densities are given as well as a Bayesian interpretation of the weight function involved. The asymptotic behavior of the tests is investigated both under the null hypothesis and under alternatives. Numerical studies are conducted to examine the performances of the criteria.