Mathematical Sciences: Custom-Designed Confidence Set Construction

数学科学：定制设计的置信集构建

• 批准号: 9224370
• 负责人: Anthony Hayter
• 金额: $ 6万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9224370&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Custom; Designed; Confidence

The objective of this project is to improve the quality of statistical inference methods available to an experimenter through the use of improved and custom-designed confidence sets. While it is clear that confidence bounds on a set of parameters are more informative to an experimenter than the answer to a hypothesis test formulation of the problem, there are many essentially basic statistical inference problems where current techniques for confidence set construction are either crude, inefficient or nonexistent. This may be because of a complicated distributional set-up, because the real parameters of interest are functions of other basic parameters, or because the experimenter has chosen to emphasize certain kinds of information such as directional decisions. In many settings, the experimenter has some clearly defined objectives which can rightly and sensibly be used to determine a sensitive and powerful inference method, yet will find out that confidence sets are currently only available for standard less specific inference approaches. The construction of custom-designed confidence sets associated with these specific inference procedures will enable the experimenter to make a fuller and more complete inference than is often currently possible. It is important to develop these techniques and to make them widely available since many decisions type inference are currently being made, such as in comparative drug trials, in which the decision results are being reported (e.g., drug A is more effective than drug B) and where, in fact, additional free information (such as a confidence interval for the difference in the efficacies of drugs A and B) is also available but is not being utilized. This research will consider ways to improve current data analysis techniques. The measurement of data and the subsequent analysis of such data inevitably involves some uncertainty, and the objective of this research is to develop improved ways of dealing with this uncertainty through the science of statistical inference. This investigation will consider both the design of experiments or data collection schemes, together with the analysis of the data. The main thrust of the research will be to develop new ways of presenting the results of statistical analyses which are designed to be clear and intiutively comprehensible to the lay person. Moreover, these methods must be accurate and they must efficiently summarize all the available information. These new techniques will be useful for researchers and experimenters in areas such as engineering, quality control, clinical trials, medical studies and other important fields.

该项目的目标是提高 实验者可用的统计推断方法 通过使用改进的和定制设计的置信度集。 虽然很明显，一组参数的置信界限 对实验者来说，比对一个问题的答案更有意义。 假设检验公式化的问题，有很多 基本的统计推断问题， 用于置信集构造的技术要么是粗糙的， 无效或不存在。 这可能是因为复杂的分布设置， 因为感兴趣的真实的参数是其它参数的函数 基本参数，或者因为实验者选择了 强调某些类型的信息，如方向 决策 在许多情况下，实验者有一些明确的 明确的目标，可以正确和明智地用于 确定一个敏感和强大的推理方法，但将 发现置信度集目前仅适用于 标准的不太具体的推理方法。建设 定制设计的置信度集与这些特定的 推理程序将使实验者作出一个 比现在更全面、更完整的推理 可能 重要的是要发展这些技术， 使它们广泛可用，因为许多决策类型推断 目前正在进行，例如在比较药物试验中， 正在报告哪些决策结果（例如，药物A是 比药物B更有效），并且事实上， 信息（例如， 药物A和B）的功效也是可获得的，但不是 被利用。 这项研究将考虑如何改善目前的数据 分析技术。 数据的测量和随后的 对这些数据的分析不可避免地涉及一些不确定性， 这项研究的目的是开发改进的方法， 通过统计学来处理这种不确定性 推论 本次调查将考虑两个设计 实验或数据收集计划，以及 数据分析。 这项研究的主要目的是 制定新的统计结果呈现方式， 分析旨在清晰直观， 对外行人来说是可以理解的。 此外，这些方法必须 准确，他们必须有效地总结所有可用的 信息. 这些新技术将有助于 研究人员和实验人员在工程等领域， 质量控制、临床试验、医学研究和其他 重要领域。