Matus Maciak (Charles University)

Quantile LASSO in Nonparametric Models with Changepoints Under Optional Shape Constraints

Nonparametric models are popular modeling tools because of their natural overall flexibility. In our approach, we apply nonparametric techniques for panel data structures with changepoints and optional shape constraints and the estimation is performed in a fully data driven manner by utilizing atomic pursuit methods – LASSO regularization techniques in particular. However, in order to obtain robust estimates and, also, to have a more complex insight into the underlying data structure, we target conditional quantiles rather then the conditional mean only. The whole estimation process and the following inference become both more challenging but the results are more useful in practical applications. The underlying model is firstly introduced and some theoretical results are presented. The proposed methodology is applied for a real data scenario and some finite sample properties are investigated via an extensive simulation study. This is a joint work with Ivan Mizera, University of Alberta and Gabriela Ciuperca, University of Lyon