Core Concepts
The author presents a statistical comparison method for random variables in multidimensional structures with varying scales, introducing the concept of Generalized Stochastic Dominance (GSD) to handle uncertainty and robustify tests.
Abstract
The content discusses the application of Generalized Stochastic Dominance (GSD) in statistical comparisons involving random variables with locally varying scales. It addresses challenges in statistics and machine learning by proposing a methodology that considers stochastic dominance under different types of uncertainties. The study introduces a regularized statistical test for GSD, emphasizing its robustness through imprecise probability models. By illustrating the approach using data from multidimensional poverty measurement, finance, and medicine, the authors aim to provide an efficient framework for analyzing systematic distributional differences within populations.
Key points include:
Introduction to spaces with locally varying scale of measurement.
Proposal of a generalized stochastic dominance order based on preference systems.
Derivation of regularized statistical tests using linear optimization techniques.
Robustification through imprecise probability models to address model uncertainty.
Application examples from multidimensional poverty measurement, finance, and medicine showcase the effectiveness of the proposed methodology.
Stats
Eπ(u ◦ X) ≥ Eπ(u ◦ Y)
R∗1 = n(x, y): xj ≥ yj ∀j ≤ r
R∗2 = ((x, y), (x′, y′)): xj − yj ≥ x′j − y′j ∀j ≤ z; xj ≥ x′j ≥ y′j ≥ yj ∀j > z