Transform orders and stochastic monotonicity of statistical functionals

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of functionals, aside from their large sample properties. We study a in terms usual order. For this purpose, we introduce generalized family orders, which referred transform showing that provides flexible framework for deriving monotonicity results. Given our general definition makes possible obtain well known ordering relations particular cases, can easily apply method different families functionals. These include prominent inequality measures, entropy, Gini index, its generalizations. also illustrate applicability approach by determining least favorable distribution, bootstrap statistics, goodness-of-fit testing procedures.