Testing for equality between two transformations of random variables

TL;DR

This paper develops a nonparametric test to determine if two unknown transformations of random variables are equal, applicable in cases with known or unknown original distributions, supported by simulations and real data analysis.

Contribution

It introduces a new nonparametric test statistic for equality of transformations, applicable to both known and unknown distribution cases, with demonstrated effectiveness.

Findings

Test maintains appropriate level in simulations

Test has good power in detecting differences

Real data example illustrates practical utility

Abstract

Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions. Second, they are unknown but observed before contaminations. We propose a nonparametric test statistic based on empirical cumulative distribution functions. Monte Carlo studies are performed to analyze the level and the power of the test. An illustration is presented through a real data set.