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.

翻译：电子变量是近年来得到显著发展的统计假设检验新方法。本文引入电子变量可逼近性方法，并利用其发展出一种通用逼近技术，使我们能够为应用中重要的常见分布类构建电子变量。电子变量最初源于算法信息论中莱文（平均有界）随机性检验的概念。我们证明所构建的电子变量可用于为分布类提供显式随机性检验的明确构造。