The Iterated Lasso for High-Dimensional Logistic Regression

We consider an iterated Lasso approach for variable selection and estimation in sparse, high-dimensional logistic regression models. In this approach, we use the Lasso (Tibshirani 1996) to obtain an initial estimator and reduce the dimension of the model. We then use the Lasso as the initial estimator in the adaptive Lasso (Zou 2006) to obtain the final selection and estimation results. We provide conditions under which this two-step approach possesses asymptotic oracle selection and estimation properties. One important aspect of our results is that the total number of covariates can be larger than the sample size. Simulation studies indicate that the iterated Lasso has superior performance in variable selection relative to the standard Lasso. A data example is used to illustrate the proposed approach.