Statistical inference in the case of unordered pairs

Abstract

The notion of symmetrized distribution is applied to clarify statistical inference for bivariate distributions when the observability of two random variables is restricted to unordered pairs. Properties of statistics based on unordered pairs are considered. Connections between independence in the ordered and unordered cases are described and used to analyze certain properties of the independence test in both cases

AMS 1980 subject classification:

• Primary 62H20
• secondary 62H15,62G10
• Codependence
• independence
• quadrant dependence
• strongly symmetric parameters and statistics
• symmetrization of distribution
• unordered pairs