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

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.