Optimal decorrelated score subsampling for high-dimensional generalized linear models under measurement constraints

Abstract

– When responses of massive data are hard to obtain due to some reasons such as privacy and security, high cost and administrative management, response-free subsampling is considered. In this paper, we propose a response-free decorrelated score subsampling approach to estimate and make statistical inference for a preconceived low-dimensional parameter in high-dimensional generalized linear models. The unconditional consistency and asymptotic normality of the resulting weighted subsample estimator are established using martingale techniques since the subsamples are no longer independent. The optimal response-free subsampling probabilities are derived based on A- and L-optimality criteria. Based on the optimal subsample, we further propose a more efficient and stable unweighted decorrelated score subsample estimator. The satisfactory performance of our proposed subsample estimators are demonstrated by simulation results and two real data applications.