Асимптотска својства непараметарских тестова заснованих на U-статистикама и V-статистикама са недегенерисаним и слабо дегенерисаним језгром

Abstract

Тестови сагласности са расподелом и тестови симетрије заузимају значајно место у непараметарској статистици...

Goodness of t and symmetry tests occupy a signicant part of nonparametric statistic. Most of classical tests are based on the distance between the assumed distribution function and its consistent estimate, empirical distribution function. The symmetry tests are analogously constructed. A new approach that is especially attractive in recent years is making tests based on characterizations of dierent types. Those tests use U-empirical distribution functions (generalized empirical ones), U-empirical transforms (eg. Laplace transform, characteristic functions etc.) and U-empirical moments of distributions. The main advantage of these tests is that they are often free of some distribution parameters. Therefore they are suitable for testing composite hypothesis.