Mathematical Sciences: Topics in Statistical Inference

该建议包含十个问题，涉及各种 研究者希望研究的统计学主题 这一时期的资金需求。 一个主要的话题， 这一建议是令人遗憾的，即，自举、折叠等 这一领域一直是作者的主要研究重点。 其他 本报告涵盖的统计领域包括：数据深度和 多变量分析，置信区域和置信带，方向 数据分析生存分析，稳健性，方差分析和 实验设计 该提案包括一些建议 概念和程序尚待探索，数学和 数字上的 本研究主要集中在一个相对较新的 统计学中的主题名为bootstrap。 这种新方法在 统计是计算机密集型的，它往往更准确， 更多的用户可以使用，因为它取代了数学劳动， 电脑工作。 这项研究的重点之一是 研究这种方法如何评估其自身 精度 在这里提出的其他研究课题中， 在生存领域发展一种非常普遍的方法 分析，这是药物研究的关键工具。 的 研究还将包括新的统计概念， 鲁棒性，一个与缺乏敏感性有关的领域（ 数据的结论相对较少 不具代表性的数据值。

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.