Generalized Fiducial Inference for Modern Statistical Problems

现代统计问题的广义基准推断

• 批准号: 0968714
• 负责人: Jan Hannig
• 金额: $ 17.09万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-03 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968714&HistoricalAwards=false
• 关键词: Generalized; Fiducial; Inference; Modern; Statistical

In this proposal the investigators revisit Fisher's controversial fiducial argument with a modern set of questions in mind. This is motivated by the success of generalized inference as introduced by Tsui & Weerahandi (1989), which in fact leads to the same results as Fisher's fiducial inference (Hannig, Iyer & Patterson, 2006). The investigators do not attempt to derive a new ``paradox free theory of fiducial inference''. Instead, with minimal assumptions, the investigators present a new simple fiducial recipe that can be applied to conduct statistical inference via the construction of generalized fiducial distributions. This recipe is inspired by the concept of generalized pivotal quantity and is designed to be fairly easily applicable in many practical applications. It can be applied regardless of the dimension of the parameter space (i.e., including nonparametric problems), and it often leads to statistical procedures that are asymptotically exact and, more importantly, possess very good approximate small sample properties. The investigators propose to investigate theoretical properties of generalized fiducial distributions for statistical problems and apply their findings to various problems of broader interest. Systematic study of properties of generalized fiducial inference will increase our understanding of foundations of statistics and will give statisticians an additional tool to use when dealing with problems they encounter in practice. More directly, successful solution of the proposed applied problems will immediately bear fruit in the application areas, e.g., pharmaceutical statistics and metrology. For instance, the U.S. Food and Drug Administration (FDA) guidance document spells out analysis procedures for demonstration of equivalence of two or more drug formulations. The investigators aim to show that the fiducial approach will lead to more efficient procedures, which will result in cost and time savings, an important issue for the drug industry. In metrology, the International Bureau of Weights and Measures (BIPM) in conjunction with the International Organization for Standardization (ISO), has published a ``Guide to Expression of Uncertainty in Measurements" (GUM) which spells out the procedures to be followed by national metrological institutes such as NIST in the US, NPL in UK, and PTB in Germany. A problem that is unique to metrology is that every measurement is subject to unknown and unknowable systematic errors that are often larger than random errors. The only way to quantify these unknowable systematic errors is via specification of subjective distributions for them. The GUM specifies how to combine data-based estimates of standard deviations for some error components in the calculations and subjective estimates of uncertainty for other error components. The investigators aim to demonstrate that the fiducial method provides a natural approach for accomplishing this. Such results are likely to influence the metrology community in modifying and improving their current procedures.

在此提案中，调查人员考虑了一系列现代的问题，回顾了费舍尔有争议的信托论点。 这是由Tsui＆Weerahandi（1989）引入的广义推论的成功所激发的，实际上，这与费舍尔的基金会推论相同（Hannig，Iyer＆Patterson，2006）。 研究人员没有试图推导新的``信托推理的悖论自由理论''。 取而代之的是，由于假设最少，研究人员提出了一种新的简单基准配方，可以通过构建通用的基准分布来进行统计推断。 该食谱的灵感来自广义关键数量的概念，其设计为相当容易地用于许多实际应用中。无论参数空间的维度如何（即包括非参数问题），都可以应用它，并且通常会导致统计程序在渐近上是渐变的，更重要的是，具有很好的近似样品属性。研究人员建议研究普遍的基准分布的理论特性，以解决统计问题，并将其发现应用于各种更广泛关注的问题。 对广义基金推断的性质的系统研究将增加我们对统计基础的理解，并在处理他们在实践中遇到的问题时为统计学家提供一种额外的使用工具。 更直接的是，提出的应用问题的成功解决方案将立即在应用领域（例如药物统计和计量学领域）中产生果实。例如，美国食品和药物管理局（FDA）指导文件阐明了分析程序，以证明两种或多种药物配方的等效性。研究人员的目的是表明，基准方法将导致更有效的程序，这将导致成本和时间节省，这对药品行业来说是一个重要的问题。 In metrology, the International Bureau of Weights and Measures (BIPM) in conjunction with the International Organization for Standardization (ISO), has published a ``Guide to Expression of Uncertainty in Measurements" (GUM) which spells out the procedures to be followed by national metrological institutes such as NIST in the US, NPL in UK, and PTB in Germany. A problem that is unique to metrology is that every measurement is subject to未知的系统错误通常比随机错误更大。计量社区修改和改善其当前程序。