Estimating residual/error distribution from regularised regression (ridge, lasso, eslastic net)

Hi there,

I'm trying to use an elastic net to fit a predictive model where I have some high correlation between my covariates. However, I really need a model for my error distribution. So just to be clear, I'm fitting a model

y=\beta X + \epsilon 

and I want the distribution of \epsilon, (it may depend on X, or at least \hat{y}).

Ideally the model would be fit taking into account this distribution, but I'll settle with a good way of estimating it after the fact for now.

Thanks.