LASSO-Type Penalization in the Framework of Generalized Additive Models for Location, Scale and Shape

For numerous applications, it is of interest to provide full probabilistic forecasts,
which are able to assign plausibilities to each predicted outcome. Therefore,
attention is shifting constantly from conditional mean models to probabilistic
distributional models capturing location, scale, shape and other aspects of
the response distribution. One of the most established models for distributional
regression is the generalized additive model for location, scale and shape
(GAMLSS). In high-dimensional data set-ups, classical fitting procedures for
GAMLSS often become rather unstable and methods for variable selection are
desirable. Therefore, a regularization approach for high-dimensional data set-ups in the framework of GAMLSS is proposed. It is designed for linear covariate effects and is based on L1-type penalties. The following three penalization options are provided: the conventional least absolute shrinkage and selection operator (LASSO) for metric covariates, and both group and fused LASSO for categorical predictors. The methods are investigated both for simulated data
and for two real data examples, namely Munich rent data and data on extreme
operational losses from the Italian bank UniCredit.