E-variables and tests of randomness for distribution classes
🤖 AI Summary
This work addresses the lack of effective randomness tests for broad classes of probability distributions by proposing a novel framework termed *e-variable-approximability*. For the first time, this approach enables the construction of computable e-variables for common distribution classes. By integrating Levin’s notion of randomness tests with approximation techniques, the method yields explicit and computable randomness tests tailored to entire distribution families. It provides both theoretical guarantees and practical testing procedures for important classes such as exponential families, thereby substantially extending the applicability of e-variables in algorithmic information theory and statistical inference.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
e-variables
randomness tests
distribution classes
statistical hypotheses
Algorithmic Information Theory
Innovation
Methods, ideas, or system contributions that make the work stand out.
e-variables
randomness tests
distribution classes
e-variable-approximability
Algorithmic Information Theory
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