Inference for high-dimensional and multivariate data

高维和多变量数据的推理

• 批准号: 0906795
• 负责人: Peter Hall
• 金额: $ 19.94万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906795&HistoricalAwards=false
• 关键词: Inference; dimensional; multivariate; data

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.

该研究计划将开发和探索参数和非参数的新方法，以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。 它将开发用于变量选择的非线性方法，以及在极高维问题中量化变量之间的关联。 它将详细讨论以经验方式定义和访问函数数据的概率密度和模式概念的问题。 涉及排名的问题在各种各样的情况下都会出现。 例如，大学或其他机构根据其表现进行排名。 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，可能会出现错误。 该研究计划将深入研究这个问题。 越来越多的实际问题需要变量选择方法，例如根据基因对疾病和死亡率的明显影响来选择基因。 该研究计划将重点关注相对复杂的情况下的这个问题，其中变量与健康问题之间的关系异常复杂。 功能数据，例如以曲线而不是数字的形式记录的数据，在评估小麦的蛋白质含量到探索气候随时间变化的特征等各种领域都会遇到。 然而，传统统计概念（例如“最可能的数据值”的概念）对于此类数据的有效程度尚不清楚。 该研究计划将消除这种模糊性。