New Working Paper
David Rügamer, Sonja Greven
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 L2-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. After addressing several issues associated with Due to the iterative nature, which can repeatedly select the same component to update, an 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 estimated using the L2-boosting selection process. We apply our framework to the prostate cancer data set and investigate the properties of our concepts in simulation studies. The most general and promising selective inference framework for L2-Boosting as well as for more general gradient-descent boosting algorithms is an sampling approach which constitutes an adoption of the recently proposed method by Yang et al. (2016).