MM Algorithm For Martingale Difference Divergence Based Estimation Of Central Mean Subspace

Estimation of the central mean subspace is an important problem in high-dimensional regression analysis,and estimating the central mean subspace via martingale difference divergence(MDD)was recently proposed as an effective method to solve such problems.In this paper,we propose a MM algorithm for estimating the central mean subspace based on martingale difference divergence(MDD).First,we rewrite the constrained MDD optimization problem as an optimization problem on the Stiefel manifold.Secondly,for the non-smoothness,we consider the perturbed version of the objective function to ensure that it is smooth and differentiable.Then we use the concavity and convexity inequalities to find the alternative function of the perturbed objective function according to the MM algorithm,and use the Newton method on the Stiefel manifold to optimize the alternative function of the perturbed objective function.Further,we also establish the convergence of MM algorithm for estimating central mean subspace based on MDD.Finally,the feasibility of our method is verified by numerical simulation and solving real data sets.