Post-selection inference

Forward Stepwise Selection is a widely used model selection algorithm. It is, however, hard to do inference for a model that is already cherry-picked. A post-selection inference method called selective inference is investigated. Beginning with very simple examples and working towards more complex ones, we evaluate the method's performance in terms of its power and coverage probability though a simulation study. The target of inference is investigated and the impact of the amount of information used to construct conditional conference intervals is investigated. To achieve the same level of coverage probability, the more conditions we use, the wider the Confidence Interval is -- the effect can be extreme. Moreover, we investigate the impact of multiple conditioning, as well as the importance of the normality assumption on which the underlying theory is based. For models with not very many parameters (p << n), we find normality is not crucial in terms of the test coverage probability.