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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759152
• 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.The primary objective of this proposal is to thoroughly study the extended empirical likelihood method through its key component, the expansion factor of the underlying composite similarity mapping, in order to strengthen its theoretical foundation and further improve its already impressive accuracy. To achieve this objective, my research will focus on identifying the optimal expansion factor through understanding its dependence on the sample size, higher moments of the underlying distribution and the dimension of the parameter vector.The secondary objective of this proposal is to work on several related projects concerning the extended empirical likelihood. These are [1] finding new applications of this method, [2] simplifying its theory and computation, and [3] studying its asymptotic behavior when the dimension of the data increases with the sample size. The impact of this research will be significant. Findings related to the primary objective will put the extended empirical likelihood method on a sound theoretical footing and substantially improve its accuracy. Results concerning the secondary objective will [i] bring more accurate inference to empirical likelihood applications that previously use the original empirical likelihood, [ii] make the method easier to use and applicable to a wider range of problems, and [iii] make it possible to apply the method to high dimensional data which is an important topic in Big Data analysis.

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）。现有的未覆盖问题的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方法的类型。 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。这是解决覆盖不足问题的主要方法。该提案的主要目标是通过其关键组成部分彻底研究扩展的经验可能性方法，即基础综合相似性映射的扩展因子，以增强其理论基础并进一步提高其已经令人印象深刻的准确性。为了实现这一目标，我的研究将着重于通过理解其对样本量的依赖性，基础分布的较高矩和参数矢量的维度来确定最佳扩展因子。该提案的次要目标是在几个有关扩展经验可能性的相关项目上工作。这些是[1]找到这种方法的新应用，[2]简化了其理论和计算，[3]当数据尺寸随样本量增加时，研究其渐近行为。这项研究的影响将很大。与主要目标相关的发现将使扩展的经验可能性方法在合理的理论基础上，并显着提高其准确性。关于次要目标的结果[i]将对以前使用原始经验可能性的经验可能性应用更加准确地推断，[ii]使该方法易于使用并适用于更广泛的问题，[iii]使得将方法应用于高维数据，这在大数据分析中是重要的主题。