This research project is in the general area of mathematical statistics and concerns topics in geometric probability, density estimation, asymptotic methods and approximate inference, decision theory, and non-parametric tilting methods. The investigation involves viable computer- intensive techniques for data analysis. A general theme of the research is the theoretical development of general purpose methods that are widely applicable to problems in statistics. This statistical research addresses problems of constructing confidence intervals for unknown parameters in statistical models. 'Automatic' percentiles methods are being developed to handle such problems, motivated by Efron's work on bootstrap confidence intervals. Based on mathematical theorems and simulation studies, the automatic methods are generally more accurate than Efron's work and are easier to implement in practice.
