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

Transform orders and stochastic monotonicity of statistical functionals