Mathematical Sciences: Investigations in Order Restricted Inference and Improved Inference Procedures

数学科学：有序限制推理和改进推理程序的研究

• 批准号: 9400476
• 负责人: Arthur Cohen
• 金额: $ 21.6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400476&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Investigations; Order; Restricted

9400476 Cohen Inference in order restricted models and improved inferences procedures will be pursued. A summary is as follows: We will pursue the study of "one sided" confidence regions and simultaneous confidence intervals for parameters that lie in a subset of k dimensional space. This problem is meaningful to the statistical practitioner. We will introduce and study the notion of cone order association. Ordinary association is linked to the cone which is the first quadrant of k dimensional space. Important applications exist where ordinary association is not good enough to obtain meaningful results but cone order association would help. We study 2 and 3 dimensional contingency tables and seek optimal tests for a wide variety of hypothesis testing problems. A list of problems concerning a wide variety of extensions of results in order restricted testing problems is also discussed. Professor Strawderman will study problems related to hierarchical Bayes models, adaptive minimax estimators, estimators which improve on truncated estimators such as the positive-part James-Stein estimator or the MLE of a positive normal mean, and minimax estimation for spherically symmetric distributions. He is also writing a monograph on multiparameter estimation with James Berger. This proposal is concerned with improved statistical inference methodology. Statistical inference typically is concerned with estimating unknown characteristics of populations or testing hypotheses about these unknown characteristics. Statistical methodology has progressed greatly over the past 60 years. Yet there is considerable room for improving procedures that will be more efficient and provide substantial savings to users of the improved procedures. This proposal is primarily devoted to developing such new and better procedures.

9400476 科恩 推理顺序限制模型和改进的推理程序将被追求。摘要如下：我们将继续研究位于k维空间子集中的参数的“单侧”置信区域和同时置信区间。这个问题对统计工作者来说是有意义的。我们将介绍和研究锥序结合的概念。通常的联想与锥相连，锥是k维空间的第一象限。 重要的应用程序存在普通协会是不够好，以获得有意义的结果，但锥序协会将有所帮助。我们研究了二维和三维列联表，并寻求各种各样的假设检验问题的最优检验。一个列表的问题有关的各种各样的扩展结果，以限制测试问题进行了讨论。Strawderman教授将研究与分层贝叶斯模型、自适应极大极小估计、改进截断估计（如正部分James-Stein估计或正态均值的极大似然估计）的估计以及球对称分布的极大极小估计相关的问题。他还与詹姆斯·伯杰（James Berger）一起撰写了一本关于多参数估计的专著。 这一建议涉及改进的统计推断方法。统计推断通常涉及估计总体的未知特征或检验关于这些未知特征的假设。 统计方法在过去60年中取得了很大进步。然而，在改进程序方面仍有很大的余地，这些程序将更加有效，并为改进后的程序的使用者节省大量费用。这项建议主要致力于发展这种新的和更好的程序。