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.
