Elicitation complexity of statistical properties

• 成果类型: Article
• 署名作者: Frongillo, Rafael M.; Kash, Ian A.
• 署名单位: University of Colorado System; University of Colorado Boulder; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa093
• 发表日期: 2021
• 页码: 857879
• 关键词: Risk measures

摘要

A property, or statistical functional, is said to be elicitable if it minimizes the expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work has sought to identify which properties are elicitable, here we investigate a more nuanced question: how many dimensions are required to indirectly elicit a given property? This number is called the elicitation complexity of the property. We lay the foundation for a general theory of elicitation complexity, which includes several basic results on how elicitation complexity behaves and the complexity of standard properties of interest. Building on this foundation, our main result gives tight complexity bounds for the broad class of Bayes risks. We apply these results to several properties of interest, including variance, entropy, norms and several classes of financial risk measures. The article concludes with a discussion and open questions.