Sparse Poisson Regression with Penalized Weighted Score Function

We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from ${\mathrm{\ell }}_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We show that under mild conditions, our estimator is ${\mathrm{\ell }}_1$ consistent and the tuning parameter can be pre-specified, which shares the same good property of the square-root Lasso.