Inference for high-dimensional and multivariate data

该研究计划将开发和探索新的方法，包括参数和非参数，以解决多变量和高维统计中的各种问题。特别是，它将研究排名的随机波动模型和评估排名的可靠性。它将开发非线性方法来选择变量，并在非常高维的问题中量化变量之间的关联。它将详细讨论以经验的方式定义和访问函数数据的概率密度和模式的概念的问题。涉及排名的问题出现在非常广泛的各种背景下。例如，根据衡量大学或其他机构表现的标准对其进行排名。然而，人们对排名的可靠性知之甚少，毕竟这些排名是基于经验证据，容易出错。研究计划将对这一问题进行深入研究。在越来越广泛的实际问题中需要变量选择的方法，例如根据基因对疾病和死亡率的明显影响来选择基因。研究计划将在相对复杂的情况下关注这一问题，在这些情况下，变量和健康问题之间的关系异常复杂。从评估小麦蛋白质含量到探索气候特征随时间变化的方式，各种领域都会遇到功能性数据，例如以曲线而不是数字的形式记录数据。然而，传统的统计概念，如“最有可能的数据值”的概念，在多大程度上适用于这种数据，目前还没有得到很好的理解。这项研究计划将消除这种模糊的现象。

The research program will develop and explore new methods, both parametric and nonparametric, for solving a variety of problems in multivariate and high-dimensional statistics. In particular it will study models for the stochastic fluctuations of rankings and for assessing the reliability of rankings. It will develop nonlinear methods for variable selection, and for quantifying the association among variables, in very high-dimensional problems. And it will take up in detail the problem of defining and accessing, in an empirical way, the notions of probability density and mode for functional data. Problems involving rankings arise in a very wide variety of contexts. Examples include the ranking of universities or other institutions on the basis of measures their performance. However, relatively little is known about the reliability of rankings, which after all are based on empirical evidence which is subject to error. The research program will study this matter in depth. Methods for variable selection are required in an increasingly wide range of practical problems, for example the selection of genes in terms of their apparent influence on disease and mortality. The research program will focus on this problem in relatively complex cases, where the relationship between the variables and health issues is unusually complex. Functional data, for example where the data are recorded in the form of curves rather than numbers, are encountered in fields as diverse as assessing the protein content of wheat to exploring ways in which the characteristics of climate change over time. However, the extent to which conventional statistical notions, such the concept of the `most likely data value,' are valid for such data is not well understood. The research program will remove this obscurity.