Title: Automatic detection of successive variable groups in a multivariate regression model
Authors: Matus Maciak - Charles University (Czech Republic) [presenting]
Abstract: A multivariate regression model is considered where the explanatory variables are naturally grouped into a series of consecutive groups. The number of variables and the number of groups can both increase with the sample size. However, most of the successive groups are assumed to be identical in terms of having the same effect on the response variable. The model ``instabilities'' occur in situations where two neighboring groups play a different role---thus, there is a sudden change with respect to the magnitude of the group effect. The idea of the proposed method is to perform an automatic detection of the different successive groups and, simultaneously, to quantify the magnitudes of the corresponding effects. The quantile check function and the fused type penalty are both combined together to obtain a robust estimate with the desired qualities. Some theoretical results are derived and the finite sample performance is investigated using a simulation study. The practical applicability of the model is illustrated with some real data examples.