Mathematical Sciences: Topics in Statistical Inference

该提案包含十个与研究者希望在寻求资金期间研究的各种统计主题有关的问题。这个提案的一个主要主题是重新采样，即bootstrap， jackknife等，这是作者研究的主要重点。这里涉及的其他统计领域包括：数据深度和多变量分析，置信区域和波段，定向数据分析，生存分析，稳健性，方差分析和实验设计。该建议包括一些已提出的概念和程序，但尚未探索，数学和数值。本文提出的研究主要集中在统计学中一个相对较新的课题——bootstrap。这种新的统计学方法是计算机密集型的，它通常更准确，更容易被更多的用户使用，因为它用计算机工作取代了数学劳动。这项研究的重点之一是调查这种方法如何评估其自身的准确性。在这里提出的其他研究主题中，是在生存分析领域发展一种非常通用的方法，这是药物研究的关键工具。研究还将包括统计稳健性的新概念，这是一个与数据结论对相对较少的不具代表性的数据值缺乏敏感性（这是期望的）有关的领域。

This proposal contains ten problems related to various statistical topics which the investigator wishes to study during the period for which this funding is sought. A dominant topic in this proposal is resampling, i.e., bootstrap, jackknife, etc, an area which has been the author's main focus of research. Other areas of statistics covered here include: data depth and multivariate analysis, confidence regions and bands, directional data analysis survival analysis, robustness, ANOVA and experimental designs. The proposal includes some proposed notions and procedures yet to be explored, mathematically and numerically. The proposed research mainly focuses on a relatively new topic in statistics named the bootstrap. This new methodology in statistics is computer intensive, it is often more accurate and accessible to more users, since it replaces mathematical labor by computer work. One of the thrusts of this research is to investigate how well this methodology can evaluate its own accuracy. Among other topics of research proposed here, is the development of a very general approach in the field of survival analysis, which is a key tool in pharmaceutical researches. The research will also include new concepts of statistical robustness, an area pertaining to the lack of sensitivity (which is desired) of data-conclusions to a relatively few unrepresentative data values.