Mathematical Sciences: Topics in Statistical Inference

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This proposal contains ten problems related to various statistical topics which the investigator wishes to study during the period for which this funding is sought. A dominant topic in this proposal is resampling, i.e., bootstrap, jackknife, etc, an area which has been the author's main focus of research. Other areas of statistics covered here include: data depth and multivariate analysis, confidence regions and bands, directional data analysis survival analysis, robustness, ANOVA and experimental designs. The proposal includes some proposed notions and procedures yet to be explored, mathematically and numerically. The proposed research mainly focuses on a relatively new topic in statistics named the bootstrap. This new methodology in statistics is computer intensive, it is often more accurate and accessible to more users, since it replaces mathematical labor by computer work. One of the thrusts of this research is to investigate how well this methodology can evaluate its own accuracy. Among other topics of research proposed here, is the development of a very general approach in the field of survival analysis, which is a key tool in pharmaceutical researches. The research will also include new concepts of statistical robustness, an area pertaining to the lack of sensitivity (which is desired) of data-conclusions to a relatively few unrepresentative data values.