Extended empirical likelihood

扩展的经验可能性

• 批准号: RGPIN-2016-03804
• 负责人: Tsao, Min
• 金额: $ 2.4万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=636023
• 关键词: Extended; empirical; likelihood

The empirical likelihood method (Owen, 2001) is a powerful non-parametric method of statistical inference with many applications. However, the empirical likelihood confidence region suffers from an under-coverage problem in that its coverage probability tends to be lower than the nominal level. The problem is particularly serious in small sample and multidimensional situations. It is partly due to the rate at which the empirical likelihood statistic converges to the limiting chi-square random variable, and partly due to the convex hull constraint embedded in the formulation of the empirical likelihood (Tsao, 2013). Existing methods for the under-coverage problem can be roughly divided into two types: those aimed at increasing the rate of convergence and those targeting the convex hull constraint. The extended empirical likelihood of Tsao (2013) and Tsao and Wu (2013) is in the latter category. It is motivated by geometrically expanding the original empirical likelihood confidence regions while preserving their data driven shape. It is a leading method for dealing with the under-coverage problem.

经验可能性方法（Owen，2001）是一种强大的非参数推断，用于与许多应用有关。但是，经验可能性置信区域遭受了覆盖不足的问题，因为其覆盖率概率往往低于标称水平。在小样本和多维情况下，问题尤其严重。这部分是由于经验可能性统计量会收敛到限制卡方随机变量的速率，部分原因是嵌入经验可能性的构造中的凸壳约束（TSAO，2013年）。现有的未覆盖问题方法可以大致分为两种类型：旨在提高收敛速度和针对凸船体约束的类型的类型。 Tsao（2013）和Tsao and Wu（2013）的扩展经验可能性属于后一类。它是通过几何扩大原始经验可能性置信区域的几何发展而动机的，同时保留其数据驱动形状。这是处理覆盖不足问题的领先方法。