Inference strategies with applications and boostrapping

这项研究主要关注帮助分析复杂数据的最佳工具的开发。例如，如何将来自不同来源的DNA微阵列数据组合在一起，显示出在统计推断精度方面可能获得的巨大收益？如何将不确定的先验信息纳入当前的估计过程？如何处理有关用于表示数据抽样过程的适当统计模型-估计器的不确定性？这些问题以及更多问题可以通过适当的统计推理工具得到更好的理解。此外，拟议的研究报告还展示了定义明确的基于数据的估计技术。这一研究方案的重点是开发和应用比现有方法执行得更好的统计推理方法。统计推断是从观测数据到其潜在机制的推理过程。收缩和经验贝叶斯方法为综合来自不同来源的数据提供了有用的技术。英国皇家统计学会通讯(1995年1月)预测，收缩和经验贝叶斯方法将是21世纪初统计研究的一个主要领域。最近，几位作者考虑了一种新的方法，以不同的方式加权分量的可能性。有趣的是，这导致了收缩类型估计器，它也在经验贝叶斯方法中占有重要地位。随着以DNA微阵列为代表的新科学技术的出现，人们突然对这些方法重新产生了兴趣。这些技术将提高知识，因为它们适用于更大类别的问题，从而扩大了我们解决卫生保健、环境计量学、工程和社会科学中高级统计推断问题的能力。

This research is primarily concerned with the development of optimal tools to help in the analysis of complex data.  For example, how can DNA microarray data from various sources be combined, showing the promise of immense possible gains in statistical inferential accuracy?  How can uncertain prior information be incorporated into the current estimation process?  How can uncertainty concerning the appropriate statistical model-estimator to use in representing the data sampling process be dealt with?    These questions, and many more, can be better understood through appropriate statistical inferential tools.   The proposed research  demonstrates well-defined data-basesd estimation techniques. The focus of this research program is on the development and application of statistical inference methodologies which performs better than the existing methods. Statistical inference is the process of reasoning from observed data back to its underlying mechanism. Shrinkage and empirical Bayes methods provide useful techniques for combining data from various sources.  B.  Efron (Newsletter of the Royal Statistical Society January, 1995) predicted that shrinkage and empirical Bayes methodology would be a major area of statistical research for the early 21st century.    More recently, several authors considered a new approach to likelihood that weigh components differentially.  Interestingly, this leads to shrinkage type estimators that also feature prominently in empirical Bayes methodology.   New scientific technology, exemplified by DNA microarrays, has suddenly revived interest in these methods. These techniques will advance knowledge because of their applicability to a larger class of problems thereby extending our ability to solve advanced statistical inference problems in health-care, environmetrics, engineering and social sciences.