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

9400476科恩推理按顺序限制的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维空间的子集中的参数的“单边”置信域和同时置信度区间。这个问题对统计从业者来说是有意义的。我们将引入和研究锥序结合的概念。普通结合被连接到k维空间的第一象限锥体上。在普通关联不足以获得有意义的结果的情况下，存在重要的应用，但锥序关联将有所帮助。我们研究2维和3维列联表，并为各种假设检验问题寻求最优检验。还讨论了顺序受限测试问题中与结果的广泛扩展有关的一系列问题。Strawderman教授将研究与分层贝叶斯模型、自适应极大极小估计、改进截断估计的估计(如正部分James-Stein估计或正正态均值的最大似然估计)以及球对称分布的极大极小估计有关的问题。他还与詹姆斯·伯杰共同撰写了一本关于多参数估计的专著。这项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。在过去的60年里，统计方法有了很大的进步。然而，有相当大的改进程序的余地，使程序更有效率，并为改进后的程序的使用者节省大量费用。这项提议主要致力于开发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.