Robust variable selection and distributed inference using t-based estimators for large-scale data

In this paper, we address the problem of performing robust statistical inference for large-scale data sets whose volume and dimensionality maybe so high that distributed storage and processing is required. Here, the large-scale data are assumed to be contaminated by outliers and exhibit sparseness. We propose a distributed and robust two-stage statistical inference method. In the first stage, robust variable selection is done by exploiting t-Lasso to find the sparse basis in each node with distinct subset of data. The selected variables are communicated to a fusion center (FC) in which the variables for the complete data are chosen using a majority voting rule. In the second stage, confidence intervals and parameter estimates are found in each node using robust t-estimator combined with bootstrapping and then combined in FC. The simulation results demonstrate the validity and reliability of the algorithm in variable selection and constructing confidence intervals even if the estimation problem in the subsets is slightly underdetermined.