For high-dimensional models with a focus on classification performance, the ℓ1-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given sample size n and a dimension of covariates p, the finite sample behavior of our proposed method with a diverging number of predictors is illustra...
