Mathematical Sciences: Statistical Theory and Methodology

这项研究项目涉及一组学者，涉及以下主题：(1)群表示的应用，(2)贝叶斯统计，(3)马尔可夫链对其平稳分布的收敛速度，(4)使用非对称最小二乘损失函数的回归百分位数，(5)在随机临床试验中使用顺应性作为协变量，(6)用于置信度的影响函数，(7)用于参数问题的更好的自动置信度区间，(8)用于‘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)管状邻域的体积和统计应用，(12)最大熵方法，(13)半线性回归中的置信域，(14)变点问题，(15)序贯检验和估计，(16)期望的近似估计，(17)复杂模型中的自举可信区间，(18)调节参数的自举选择和适应，以及(19)通过最不有利的族对参数模型的近似推断。这个项目的总体目标是发展应用数学感兴趣的新的统计理论和方法。这项研究涉及到传统数理统计和现代计算方法的结合。具体目标是理解比传统使用的更复杂的模型，并尽可能使日常使用的统计程序自动化。

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.