Regularization with Categorical Covariates: Generalizations and Extensions

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The challenge in statistical modelling of categorical variables is the high number of parameters involved. Even if the number of variables considered is only modest the number of parameters that are necessary to specify a model can be high in particular, if the investigated discrete variables have many different levels. Such high-dimensional parameter spaces cause problems when estimating the model and interpreting the results. To attack these problems, specific regularization techniques have been proposed. So far, however, these methods only work for rather simple settings with very restrictive assumptions, as (approximately) normally distributed outcomes and statistically independent observations. Since these assumptions are often violated in practice, the goal of the intended project is to generalize and extend regularization approaches for categorical covariates to make sure that these promising methods can be used in interesting applications in the applied sciences.