Non-negative Constrained Penalty for High-Dimensional Correlated Data

In this paper, we investigate five estimators for high-dimensional correlated data with the non-negative constraints on the coefficients, which are nnMnet, nnSnet, nnSace, nnGsace and nnSsace estimators. Specifically, three commonly used penalties: Mnet, smooth adjustment for correlated effects (Sace), and generalized smooth adjustment for correlated effects (Gsace), under which three non-negative penalty estimators, nnMnet, nnSace and nnGsace are proposed, accordingly. Similar to the nnMnet and nnGsace estimators, we further combine the Scad penalty function with Liu estimator and Ridge estimator to propose non-negative Snet (nnSnet) and non-negative Ssace (nnSsace), respectively. For non-negative variable selection, we give two algorithms, fast active set block coordinate descent algorithm and one-step estimator with coordinate descent algorithm. Furthermore, we demonstrate the consistency of variable selection and estimation error bounds for the nnSace estimator, and the oracle non-negative biased estimator property for nnMnet, nnSnet, nnGsace and nnSsace estimators, respectively. Finally, we show the advantages of the proposed method through some simulations and apply our method on stock data.