Mathematical Sciences: Prediction Theory, Asymptotic Distributions of Eigenvalues, Confidence Set Validity

本研究课题包括三个问题。 第一 处理预测理论和不正确的先验。 目标是 从不适当的先验中找到可用的推理程序， 其将具有某些最佳性质。 第二个问题 将找到随机特征值的渐近分布 对称矩阵 第三个问题是建设 线性回归函数的置信区间 参数 这样的置信区间是由渐近 参数，因此可计算的严格上界和下界是 难找到像 首席研究员将开发此类 界限。

The research project consists of three problems. The first deals with prediction theory and improper priors. The goal is to find usable inferential procedures starting from improper priors, which will have certain optimal properties. The second problem will find asymptotic distribution of eigenvalues of random symmetric matrices. The third problem is that of construction of confidence intervals for linear functions of regression parameters. Such confidence intervals are found by asymptotic arguments and hence computable tight upper and lower bounds are hard to find. The principal investigator will develop such bounds.