Mathematical Sciences: Advances in Resampling and Data-Depth

本研究涉及重采样和数据深度领域的六个子主题：bootstrap的鲁棒化；基于重采样和数据深度的二阶平衡置信区域和置信带；半参数模型与自举；生物等效性重采样；推理频谱;以及基于数据深度的描述性统计和推断。在过去的十年中，这些领域一直是研究者的主要研究重点。特别是Efron的引导是整个研究的主导主题。研究可能看起来是数学性质的，但是对统计方法的潜在影响一直是选择这些研究问题的关键因素。数据深度的概念除了具有独立的意义外，在自举方法中也有重要的应用。数据深度在多元描述统计中的应用正在研究中得到进一步的探索。Bootstrap是统计学中的一项新技术，由b.e fron于1979年发现，在80年代和90年代取得了巨大的进步。这个PI从这一发现的早期就参与了这些进展。Bootstrap几乎在统计科学的每个领域都产生了影响，本研究旨在进一步发展。本研究包含的一个想法是，当调查中的一些回答缺失时，使用bootstrap构建统计结论谱。这项研究的另一个重点是当数据有很多很多组成部分时，图像和其他类型的摘要。后一项研究是基于所谓的数据深度，它本质上是相对于数据云整体的数据中心的度量。其他主题涉及当方法过于计算机密集时的高效计算。

DMS 9624940 Singh This research is on six subtopics in the area of resampling and data-depth: robustification of the bootstrap; second order balanced confidence regions and bands based on resampling and data depth; semiparamtric models and the bootstrap; resampling on bioequivalence; inference spectrum; and descriptive statistics and inferences based on data-depth. These areas have been the investigator's main focus of research in the past decade. Efron's bootstrap in particular is the dominant subject throughout the research. The research may seem mathematical in nature, however the potential impact on statistical methodology has been the key factor in the selection of these research problems. Besides being of independent interest, the notion of data-depth has an important application in bootstrap methodology. The use of data-depth in multivariate descriptive-statistics is being further explored in the research. Bootstrap is a new technology in statistics, discovered by B. Efron in 1979, which has made tremendous advances in the eighties and the nineties. This PI has been involved with these advances since the early years of this discovery. Bootstrap has had impact in nearly every area of statistical sciences and this research is geared toward its further advancement. One of the ideas included in this research is the construction of a spectrum of statistical conclusions using bootstrap when some of the responses in a survey are missing. One other thrust of this research is towards pictorial and other types of summaries when data have many, many components. The latter research is based on what is known as data-depth, which is essentially a measure of centrality of a datum with respect to the totality of the data-cloud. Other topics involve efficient computing when a methodology is too computer intensive.