  We proposed a new penalized method in this paper to solve sparse Poisson
Regression problems. Being different from $\ell_1$ 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 $\ell_1$
consistent and the tuning parameter can be pre-specified, which shares the same
good property of the square-root Lasso.
