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

9400476科恩推理在顺序限制模型和改进的推理程序将继续进行。总结如下：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。这个问题对统计从业者很有意义。我们将介绍和研究锥阶关联的概念。普通的关联与k维空间的第一象限的锥相关联。在一些重要的应用中，普通的关联不足以获得有意义的结果，但锥形顺序关联会有所帮助。我们研究二维和三维列联表，并为各种各样的假设检验问题寻求最优检验。本文还讨论了一系列与结果的各种扩展有关的问题。Strawderman教授将研究与层次贝叶斯模型相关的问题，自适应极大极小估计量，改进截断估计量的估计量，如正部分James-Stein估计量或正正态均值的最大似然估计量，以及球对称分布的极大极小估计。他还与詹姆斯·伯杰（James Berger）合著了一本关于多参数估计的专著。本建议涉及改进统计推断方法。统计推断通常涉及估计群体的未知特征或检验关于这些未知特征的假设。统计方法在过去的60年里有了很大的进步。然而，仍有相当大的空间可以改进程序，以提高效率，并为改进程序的用户节省大量费用。这项建议主要致力于发展这种新的和更好的程序。

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.