Parallel subgroup analysis of high-dimensional data via M-regression.

It becomes an interesting problem to identify subgroup structures in data analysis as populations are probably heterogeneous in practice. In this paper, we consider M-estimators together with both concave and pairwise fusion penalties, which can deal with high-dimensional data containing some outliers. The penalties are applied both on covariates and treatment effects, where the estimation is expected to achieve both variable selection and data clustering simultaneously. An algorithm is proposed to process relatively large datasets based on parallel computing. We establish the convergence analysis of the proposed algorithm, the oracle property of the penalized M-estimators, and the selection consistency of the proposed criterion. Our numerical study demonstrates that the proposed method is promising to efficiently identify subgroups hidden in high-dimensional data.