General Empirical Processes (FWOTM641)

This project deals with empirical processes which are an important class of stochastic processes. We are interested in some theoretical properties of empirical processes and we are also plannning to look at some possible applications. In the theoretical part of this project we will focus on so-called exponential inequalities for general empirical processes. These inequalities have proven to be very powerful and useful. However their applicability stays within the reach of countable function classes and independent observations. We want to investigate whether generalizations to bigger function classes and/or to dependent observations are possible. Once this has been done, we look what at the possible consequences for some standard applications of empirical processes such as density estimation. Another part of this project is devoted to studying empirical processes based on time dependent data.

Keywords:AATO, WISK, DWIS, CAMP, TWIS, ALG, Mathematics

Disciplines:General mathematics