A high-dimensional M-estimator framework for bi-level variable selection

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and can appear either at the group level or within certain groups. such cases, an ideal model should be able to encourage variable selection consistently. Bi-level has become even more challenging have heavy-tailed distribution outliers exist in random errors covariates. this paper, we study a framework of M-estimation for selection. This encourages through computationally efficient two-stage procedure. theory, provide sufficient conditions under which our penalized M-estimator possesses simultaneous local estimation consistency if nonconvex penalty functions are used level. Both simulation studies real analysis demonstrate satisfactory finite sample performance proposed estimators different irregular settings.