Mathematical Sciences: Topics in Decision Theory and Multivariate Analysis

研究集中在可受理性领域 从不适当的先验分布中获得的决策规则， 随机变量奇异值的渐近分布理论 矩阵和浓度不等式及其应用 线性模型 决策规则的评价与比较 从不适当的先验分布获得的是目标的 研究受理。将开发一种技术来找到 随机矩阵奇异值渐近分布 这与最近开发的一种技术类似， 对称对称双曲正切函数特征值的渐近分布 随机矩阵集中不等式是一个重要的工具 在获得一些操作特性的界限时， 统计程序。 新的集中不平等将是 它可以应用于线性模型。

The research is concentrated in the areas of admissibility of decision rules obtained from improper prior distributions, asymptotic distribution theory for singular values of random matrices, and concentration inequalities with applications in linear models. The evaluation and comparison of decision rules obtained from improper prior distributions is the goal of the research on admissibility. A technique will be developed to find the asymptotic distribution of singular values of random matrices which is similar to a recently developed technique for finding the asymptotic distribution of the eigenvalues of symmetric random matrices. Concentration inequalities are an important tool in obtaining bounds on the operating characteristics of some statistical procedures. New concentration inequalities will be developed which may be applied in linear models.