Some problems in nonparametric statistics

非参数统计中的一些问题

• 批准号: 1301377
• 负责人: Thomas Chun Man Lee
• 金额: $ 24万
• 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: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301377&HistoricalAwards=false
• 关键词: Some; problems; nonparametric; statistics

The research program will draw together a wide range of new ideas for developing solutions to diverse practical problems, involving both very high-dimensional settings, where the number of components is much larger than sample size, and also contexts where dimension is much smaller than sample size. Direct benefits will accrue from addressing these cases together, not least through the development of new statistical theory. That aspect, among others, will give the program the authority it needs to carry individual research projects beyond the confines of their particular, immediate applications. Specifically, the program will introduce new ways of fitting diverse and virtually assumption-free models in the presence of measurement error. It will also introduce highly accurate ways of clustering data in the form of random functions; it will propose new, practicable ways of constructing confidence intervals; it will develop new techniques for modelling complex relationships in vector-valued data; it will introduce new resampling methods for very high-dimensional data; and it will show that models based on relatively strict assumptions can be used to motivate methodology that is largely assumption-free.

该研究计划将为开发解决各种实际问题的解决方案提供广泛的新思路，包括非常高维的设置，其中组件数量远远大于样本量，以及维度远小于样本量的环境。通过共同解决这些问题，尤其是通过发展新的统计理论，将产生直接效益。这一方面，以及其他方面，将赋予该项目所需的权威，使其能够在特定的、直接的应用范围之外开展个人研究项目。具体来说，该方案将引入新的方法来拟合多样化和几乎假设自由的模型在测量误差的存在。它还将以随机函数的形式引入高度精确的数据聚类方法；它将提出新的、可行的构造置信区间的方法；它将开发新的技术来模拟向量值数据中的复杂关系；它将为非常高维的数据引入新的重采样方法；它将表明，基于相对严格的假设的模型可以用来激励基本上没有假设的方法。