Selective inference in linear regression

We consider inference after model selection in linear regression problems, specifically after fitting the LASSO. A classical approach to this problem is data splitting, using some randomly chosen portion of the data to choose the model and the remaining data for inference in the form of confidence intervals and hypothesis tests. Viewing this problem in the framework of selective inference, conditional on a selection event, we describe other randomized algorithms with similar guarantees to data splitting, at least in the parametric setting. Time permitting, we describe analogous results for statistical functionals obeying a CLT in the classical fixed dimensional setting.