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Title: Distributional regression models with automatic variable selection Authors:  Meadhbh ONeill - University of Limerick (Ireland) [presenting]
Kevin Burke - University of Limerick (Ireland)
Abstract: Automatic variable selection and parameter estimation are performed simultaneously by our proposed distributional regression framework. This flexible method naturally adapts to heteroscedasticity in the data by allowing covariates to enter the model through multiple distributional parameters at the same time (e.g., location and scale). Automatic variable selection is performed using an information criterion that is optimized directly. The typical challenge of tuning parameter selection in lasso-type problems is circumvented, since the penalty parameter is known from the outset, e.g., it is log(n) for the BIC. As there are multiple regression components in the distributional regression setting (and, hence, each distributional parameter may have its own separate tuning parameter), our smooth information criterion is particularly computationally advantageous, since the tuning parameters are known and fixed from the start. This avoids the computationally demanding two-dimensional grid search that is typically carried out. Furthermore, the smooth (differentiable) penalty enables standard Newton Raphson optimization to be employed, making our approach more straightforward to implement than existing procedures. We will show that the method performs favourably in simulation studies and on real data.