Multivariate variable selection by means of null-beamforming

This article aims to use beamforming, a covariate-assisted data projection method to solve the problem of variable selection for multivariate random-effects regression models. The new approach attempts to explore the covariance structure in the data with a small number of random-effects covariates. The basic premise behind the proposal is to scan through a covariate space with a series of forward filters named null-beamformers; each is tailored to a particular covariate in the space and resistant to interference effects originating from other covariates. Applying the proposed method to simulated and real multivariate regression data, we show that it can substantially outperform the existing methods of multivariate variable selection in terms of sensitivity and specificity. A theory on selection consistency is established under certain regularity conditions.