Mathematical Sciences: Statistical Theory and Methodology

这个研究项目涉及一个学者团队， （1）群的应用 表示，（2）贝叶斯统计，（3） 马尔可夫链收敛到它们的平稳分布， (4)使用非对称最小二乘损失的回归拟合 函数，（5）使用依从性作为随机化中的协变量 临床试验，（6）置信限的影响函数， (7)更好的参数自动置信区间 问题，（8）“混乱情况”的排列测试，（9） 极小极大估计，（10）损失和风险估计，（11）体积 管状邻域和统计应用，（12） 最大熵方法，（13）半线性置信域 回归，（14）变点问题，（15）序贯检验和 估计，（16）期望的近似估计，（17） 复杂模型中的bootstrap置信区间，（18）bootstrap 调谐参数的选择和自适应，以及（19）近似 通过最不利族对参数模型进行推断。 该项目的总体目标是开发新的 应用统计理论与方法 数学 这项研究涉及传统的 数理统计和现代计算方法。 特别的目标是理解更复杂的模型 都是传统上使用的，并且尽可能地自动化 日常使用的统计程序。

This research project involves a team of scholars involved in the following topics: (1) applications of group representations, (2) Bayesian statistics, (3) rates of convergence of Markov chains to their stationary distributions, (4) regression percentiles using an asymmetric least squares loss function, (5) using compliance as a covariate in a randomized clinical trial, (6) influence functions for confidence limits, (7) better automatic confidence intervals for parametric problems, (8) permutation tests for 'messy situations', (9) minimax estimation, (10) loss and risk estimation, (11) volumes of tubular neighborhoods and statistical applications, (12) maximum entropy methods, (13) confidence regions in semilinear regression, (14) change-point problems, (15) sequential tests and estimates, (16) the approximate evaluation of expectations, (17) bootstrap confidence intervals in complex models, (18) bootstrap choice of tuning parameters and adaptation, and (19) approximate inference for parametric models via least favorable families. The general aim of this project is the development of new statistical theory and methodology of interest to applied mathematics. The research involves a combination of traditional mathematical statistics and modern computational methods. Particular goals are understanding more complicated models than are traditionally used and automating insofar as possible statistical procedures for routine use.