Inference for high-dimensional and multivariate data

该研究计划将开发和探索参数和非参数的新方法，用于解决多元和高维统计中的各种问题。特别是，它将研究排名随机波动和评估排名可靠性的模型。它将发展变量选择的非线性方法，以及在非常高维的问题中量化变量之间的关联。它将以经验的方式详细讨论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各种各样的环境中。例子包括大学或其他机构在衡量其表现的基础上的排名。然而，人们对排名的可靠性知之甚少，毕竟排名是基于经验证据的，容易出错。这个研究计划将深入研究这个问题。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进行选择。研究计划将集中在相对复杂的情况下，其中变量和健康问题之间的关系是异常复杂的问题。功能性数据，例如以曲线而不是数字的形式记录的数据，在各种领域都遇到过，从评估小麦的蛋白质含量到探索气候特征随时间变化的方式。然而，传统的统计概念，如“最可能的数据值”的概念，在多大程度上对这些数据有效，还没有得到很好的理解。这项研究计划将消除这种隐晦。

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.