Some problems in nonparametric statistics

该研究计划将汇集广泛的新想法，为各种实际问题制定解决方案，既涉及非常高维的环境，其中组件的数量远远大于样本大小，也涉及维度远小于样本大小的背景。共同解决这些问题将带来直接的好处，尤其是通过发展新的统计理论。除其他方面外，这一方面将赋予该计划所需的权威，使其能够进行超出其特定的、直接的应用范围的个别研究项目。具体地说，该计划将引入新的方法，在存在测量误差的情况下拟合各种几乎没有假设的模型。它还将介绍以随机函数形式对数据进行高精度分类的方法；它将提出构建可信区间的新的、可行的方法；它将开发对矢量值数据中的复杂关系进行建模的新技术；它将为非常高维的数据引入新的重新抽样方法；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不需要假设的方法。

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.