Branching into uncertainty

Abstract

Random Forests are widely used due to their flexibility and strong predictive performance, yet statistical inference and the treatment of missing or hierarchically structured data remain challenging. This dissertation addresses these challenges in three contributions. First, asymptotic properties of the Random Forest Permutation Importance Measure are investigated, and a central limit theorem is established, providing a theoretical foundation for statistical inference on variable importance. Second, inference for permutation importance in the presence of missing data is studied, with particular emphasis on the construction of confidence intervals. Third, tree-based multiple imputation methods are adapted to hierarchical data and systematically evaluated in a simulation study. Together, these contributions extend the applicability of Random Forest methodology beyond prediction and provide theoretical and practical tools for uncertainty quantification, inference, and imputation in complex data settings.