A novel regularization method for estimation and variable selection in multi-index models

Multi-index models have attracted much attention recently as an approach to circumvent the curse of dimensionality when modeling high-dimensional data. This paper proposes a novel regularization method, called MAVE-glasso, for simultaneous parameter estimation and variable selection in multi-index models. The advantages of the proposed method include transformation invariance, automatic variable selection, automatic removal of noninformative observations, and row-wise shrinkage. An efficient row-wise coordinate descent algorithm is proposed to calculate the estimates. Simulation and real examples are used to demonstrate the excellent performance of MAVE-glasso.