Mathematical Sciences: Advances in Resampling and Data-Depth

DMS 9624940 Singh这项研究是关于重采样和数据深度领域的六个子主题：Bootstrap的健壮化；基于重采样和数据深度的二阶平衡置信域和带；半参数模型和Bootstrap；生物等效性的重采样；推理光谱；以及基于数据深度的描述性统计和推断。在过去的十年里，这些领域一直是研究人员的主要研究重点。特别是埃夫隆的自举是整个研究的主导主题。这项研究可能看起来像是数学性质的，但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。除了具有独立意义之外，数据深度的概念在Bootstrap方法中也有重要的应用。数据深度在多变量描述性统计中的使用在研究中正在进一步探索。Bootstrap是由B.Efron于1979年发现的一种统计学新技术，在80年代和90年代取得了巨大的进步。从这一发现的早期起，这位PI就参与了这些进展。Bootstrap在统计科学的几乎每一个领域都产生了影响，这项研究正在为它的进一步发展做准备。这项研究中包含的一个想法是，当调查中的一些回答缺失时，使用Bootstrap构建一系列统计结论。这项研究的另一个重点是当数据有很多很多组成部分时，倾向于图片和其他类型的摘要。后一项研究是基于所谓的数据深度，数据深度本质上是衡量数据相对于整个数据云的中心性的度量。其他主题涉及当一种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.