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.
