(1) Department of Mathematical Science, Faculty of Engineering Science, Osaka University, 560 Toyonaka, Japan
Abstract:
This paper considers the problem for testing symmetry of a distribution inRm based on the empirical distribution function. Limit theorems which play important roles for investigating asymptotic behavior of such tests are obtained. The limit processes of the theorems are multiparameter Wiener process. Based on the limit theorems, nonparametric tests are proposed whose asymptotic distributions are functionals of a multiparameter standard Wiener process. The tests are compared asymptotically with each other in the sense of Bahadur.