to be honest we just recorded the coeff values for each replicate and did the bootstrap variance calculation.
% of replicates with (coef==0) is potentially much more clever, especially since that's the test we want to perform anyway. i'll run that over the data and see what changes.
I think the question is these don't look like NormalCDF(coef/se) p-values given the coef and se you report. They tend to be too small.
From a frequentist perspective, counting zeroes don't make much sense because under the null of coef=0 there is still a chance you don't estimate coef=0, even after regularization.
% of replicates with (coef==0) is potentially much more clever, especially since that's the test we want to perform anyway. i'll run that over the data and see what changes.