OPTIMAL SUBSAMPLING ALGORITHMS FOR BIG DATA REGRESSIONS

To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of estimator from a general subsampling algorithm are established, optimal probabilities A- L-optimality criteria derived. Furthermore, using Frobenius norm matrix concentration inequalities, finite sample properties subsample based on also Since depend full data estimate, an adaptive two-step is developed. Asymptotic optimality established. proposed methods illustrated evaluated through numerical experiments simulated real datasets.