LASSO Regression - p-values and coefficients I've run a LASSO in R using cv.glmnet. I would like to generate p-values for the coefficients that are selected.
I found the boot.lass.proj to produce bootstrapped p-values 
https://rdrr.io/rforge/hdi/man/boot.lasso.proj.html
While the boot.lasso.proj program produced p-values, I assume it is doing its own lasso - but I'm not seeing a way to get the coefficients.
Would it be safe to use the p-values from hdi for the coefficients produced by cv.glmnet?
 A: To expand on what Ben Bolker notes in a comment on another answer, the issue of what a frequentist p-value means for a regression coefficient in LASSO is not at all easy. What's the actual null hypothesis against which you are testing the coefficient values? How do you take into account the fact that LASSO performed on multiple samples from the same population may return wholly different sets of predictors, particularly with the types of correlated predictors that often are seen in practice? How do you take into account that you have used the outcome values as part of the model-building process, for example in the cross-validation or other method you used to select the level of penalty and thus the number of retained predictors?
These issues are discussed on this site. This page is one good place to start, with links to the R hdi package that you mention and also to the selectiveInference package, which is also discussed on this page. Statistical Learning with Sparsity covers inference for LASSO in Chapter 6, with references to the literature as of a few years ago.
Please don't simply use the p-values returned by those or any other methods for LASSO as simple plug-and-play results. It's important to think why/whether you need p-values and what they really mean in LASSO. If your main interest is in prediction rather than inference, measures of predictive performance would be much more useful to you and to your audience.
