In Defense of the Indefensible: A Very Naïve Approach to High-Dimensional Inference

A great deal of interest has recently focused on conducting inference the parameters in a high-dimensional linear model. In this paper, we consider simple and very naïve two-step procedure for task, which (i) fit lasso model order to obtain subset variables, (ii) least squares lasso-selected set. Conventional statistical wisdom tells us that cannot make use standard tools resulting (such as confidence intervals p-values), since peeked at data twice: once running lasso, again fitting However, show under certain set assumptions, with high probability, variables selected by is identical one noiseless hence deterministic. Consequently, approach can yield asymptotically valid inference. We utilize finding develop interval, be used draw regression coefficients well score test, test hypotheses regarding full-model coefficients.