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.

该研究计划将汇集各种新想法，以开发解决各种实际问题的解决方案，涉及非常高维的设置，其中组件的数量远大于样本量，而且尺寸比样本量小得多的上下文。 直接的好处将通过共同解决这些案例，尤其是通过开发新的统计理论。 该方面将为该计划赋予该计划所需的权威，以将单个研究项目范围超出其特定，即时应用的范围。具体而言，该计划将在存在测量误差的情况下引入新的方法，以拟合多种多样的，几乎没有假设的模型。 它还将以随机函数的形式引入高度准确的聚集数据的方式；它将提出构建置信区间的新的，可行的方法；它将开发用于建模矢量值数据中复杂关系的新技术；它将引入新的重采样方法，以实现非常高度的数据。它将表明，基于相对严格的假设的模型可用于激励很大程度上没有假设的方法。