E-variables and tests of randomness for distribution classes
Information Theory
2026-03-04 v1 Logic in Computer Science
math.IT
Logic
Statistics Theory
Statistics Theory
Abstract
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to develop a general approximation technique allowing us to construct e-variables for popular distribution classes important for applications. E-variables were originally based on a concept of Levin's (average-bounded) randomness tests from Algorithmic Information Theory. We show that our construction of e-variables can be used to provide an explicit construction for a randomness test with respect to a class of distributions.
Cite
@article{arxiv.2603.02492,
title = {E-variables and tests of randomness for distribution classes},
author = {Georgii Potapov and Yuri Kalnishkan},
journal= {arXiv preprint arXiv:2603.02492},
year = {2026}
}