Optimal Poisson subsampling decorrelated score for high-dimensional generalized linear models.

For high-dimensional generalized linear models (GLMs) with massive data, this paper investigates a unified optimal Poisson subsampling scheme to conduct estimation and inference for prespecified low-dimensional partition of the whole parameter. A Poisson subsampling decorrelated score function is proposed such that the adverse effect of the less accurate nuisance parameter estimation with slow convergence rate can be mitigated. The resultant Poisson subsample estimator is proved to enjoy consistency and asymptotic normality, and a more general optimal subsampling criterion including A- and L-optimality criteria is formulated to improve estimation efficiency. We also propose a two-step algorithm for implementation and discuss some practical issues. The satisfactory performance of our method is validated through simulation studies and a real dataset.