This paper discusses asymptotic and bootstrap inference methods for a set of inequality and progressivity indices. The application of non-degenerate U-statistics theory is described, particularly through the derivation of the Suits-progressivity index distribution. We have also provided formulae...

The asymptotics of large deviation probabilities for two-sample non degenerate von Mises functionals and U- statistics of arbitrary degree is investigated. We find explicitly the main term of this asymptotics. Some examples motivated by nonparametric statistics are given. The result may be...

Many well-known goodness-of-fit and symmetry tests are based on U- et V-statistics. Recent progress in the analysis of their large deviations enables to find new expressions for their local Bahadur efficiency in case of bounded kernels and to formulate the conditions of local optimality. For...

Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define suitable studentized versions of such estimating functions and consider asymptotic approximations as well as an estimating function bootstrap...