This research aims to further the understanding of, and to improve upon, the existing methodology for some important problems of statistical estimation and hypothesis testing. These problems encompass nonparametric estimation and testing, regression analysis, and the analysis of survey and spatial data. The main tools to be used fall under the category of data resampling. The chief techniques involve asymptotic expansion, combinatoric analysis, probability theory, and numerical computing. This research in the field of statistics applies new mathematical and computational tools to expand existing theory. The results should allow more efficient use of resources in the future planning of and analysis of data from statistical experiments and sample surveys.
