On the optimality of coin-betting for mean estimation

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2025-09-01 DOI:10.1016/j.ijar.2025.109550

Eugenio Clerico

引用次数: 0

Abstract

We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.

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基于均值估计的投币最优性研究

考虑一个有界实随机变量均值的检验问题。我们引入了e变量和e过程的最优类的概念，并在基于e变量的算法框架中建立了用于测试和估计（条件）均值的投币公式的最优性。因此，我们为这个测试问题提供了所有有效e变量和e过程的直接和明确的特征。用经典统计决策理论的语言，充分描述了所有允许e变量和e过程的集合，并识别了相应的最小完全类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

期刊介绍： The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.