I'm using Lasso for feature selection in a relatively low dimensional setting (n >> p). After fitting a Lasso model, I want to use the covariates with nonzero coefficients to fit a model with no penalty. I'm doing this because I want unbiased estimates which Lasso cannot give me. I'd also like p-values and confidence intervals for the unbiased estimate.
I'm having trouble finding literature on this topic. Most of the literature I find is about putting confidence intervals on the Lasso estimates, not a refitted model.
From what I've read, simply refitting a model using the whole dataset leads to unrealistically small p-values/std errors. Right now, sample splitting (in the style of Wasserman and Roeder(2014) or Meinshausen et al. (2009)) seems to be a good course of action, but I'm looking for more suggestions.
Has anyone encountered this issue? If so, could you please provide some suggestions.