The group will focus on the development and the theoretical analysis of goodness-of-fit methods and of change-point methods, always with a view towards applications and computational novelty.
In goodness-of-fit methods starting from the standard i.i.d. situation, the range of problems of potential interest will cover non-identically distributed structures as well as models involving dependence, both with continuous and discrete data. Besides procedures within the purely parametric context, the group takes an interest in semi-parametric and non-parametric testing (such as testing for symmetry, independence and the k- sample problem, among others) within modern statistical structures.
Also in the problem of change-point detection which arises in various situations, there is an urgent need of effective and relatively simple procedures that allow to make relevant inference. There are still many open problems to be solved, particularly for dependent high- dimensional setups, multiple changes, etc. Construction of good statistical procedures, derivation of theoretical results providing statistical properties as well effective computational algorithms are the main issues.