Dr. Jason Lee(Stanford University)

Title: Selective Inference via the Condition on Selection Framework: Applications to Inference After Variable Selection

Abstract: 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.