Nonparametric (NP) statistical methods are a toolbox of data analysis techniques, used when no simplifying model assumptions can be imposed on the data generating process.
Unlike for univariate data, no widely accepted unified approach to the NP analysis of multivariate datasets is available. In this project we intend to study a major concept intensively discussed in statistics: data depth. Using depth, NP methods for multivariate data can be devised. The theory of depth is, however, severely underdeveloped.
In preliminary research, we found that in parts of advanced mathematics, methods of surprising similarity to data depth have been in use for decades. Those were developed independently of the research in statistics. We plan to study these inter-connections thoroughly, and establish solid mathematical background for the depth, and for the NP analysis of complex data.
A document with a brief description of several open problems in the field that will be studied within the project.