Selective Inference is the problem of testing hypotheses that are chosen or suggested by the
data. Inference after variable selection in high-dimensional linear regression is a common
example of selective inference; we only estimate and perform inference for the selected
variables. We propose the Condition on Selection framework, which is a framework for
selective inference that allows selecting and testing hypotheses on the same dataset. In the
case of inference after variable selection (variable selection by lasso, marginal screening, or
forward stepwise), the Condition on Selection framework allows us to construct confidence
intervals for regression coefficients, and perform goodness-of-fit testing for the selected model.
This is done by deriving the distribution of the test statistic conditioned on the selection event.