Selective Inference for L_2-Boosting
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We review several recently proposed post-selection inference frameworks and assess their transferability to the component-wise functional gradient descent algorithm (CFGD) under normality assumption for model errors, also known as L_2-Boosting. The CFGD is one of the most versatile toolboxes to analyze data as it scales well to high-dimensional data sets, allows for a very flexible definition of additive regression models and incorporates inbuilt variable selection. Due to the iterative nature, which can repeatedly select the same component to update, a statistical inference framework for component-wise boosting algorithms requires adaptations of existing approaches; we propose tests and confidence intervals for linear, grouped and penalized additive model components selected by L_2-Boosting. We apply our framework to the prostate cancer data set and investigate the properties of our concepts in simulation studies.
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