Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net
This work addresses variable selection for high-dimensional data, such as in finance, but is incremental as it builds on existing elastic net methods.
The authors tackled variable selection and regularization in high-dimensional sparse linear models by introducing the ARGEN penalty method, which extends the elastic net and shows improved performance in simulations and an S&P 500 tracking application.
We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied. We also propose an algorithm called MU-QP-RR-W-$l_1$ to efficiently solve ARGEN. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. Finally an application of S&P 500 index tracking with constraints on the stock allocations is performed to provide general guidance for adapting ARGEN to solve real-world problems.