Some problems in nonparametric statistics

该研究计划将汇集各种新的想法，用于开发各种实际问题的解决方案，涉及非常高维的设置，其中组件的数量远远大于样本量，以及维度远小于样本量的上下文。 共同解决这些问题将产生直接的好处，尤其是通过发展新的统计理论。 这一方面，除其他外，将给予该计划所需的权力，使个别研究项目超越其特定的，直接的应用范围。具体来说，该计划将引入新的方法来拟合不同的和几乎无干扰的模型，在测量误差的存在。 它还将介绍以随机函数的形式将数据分组的高度准确的方法;它将提出构建置信区间的新的切实可行的方法;它将开发模拟矢量值数据中复杂关系的新技术;它将介绍非常高维数据的新的重新排列方法;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是免费的方法。

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.