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

本研究项目由三个问题组成。第一个涉及预测理论和不正当的先例。目标是从不正确的先验开始寻找可用的推理过程，这些过程将具有某些最佳性质。第二个问题是求随机对称矩阵的特征值的渐近分布。第三个问题是回归参数的线性函数的可信区间的构造问题。这样的置信度区间是通过渐近参数找到的，因此很难找到可计算的紧凑的上下界。首席调查员将制定这样的界限。

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.