  Nonuniform subsampling methods are effective to reduce computational burden
and maintain estimation efficiency for massive data. Existing methods mostly
focus on subsampling with replacement due to its high computational efficiency.
If the data volume is so large that nonuniform subsampling probabilities cannot
be calculated all at once, then subsampling with replacement is infeasible to
implement. This paper solves this problem using Poisson subsampling. We first
derive optimal Poisson subsampling probabilities in the context of
quasi-likelihood estimation under the A- and L-optimality criteria. For a
practically implementable algorithm with approximated optimal subsampling
probabilities, we establish the consistency and asymptotic normality of the
resultant estimators. To deal with the situation that the full data are stored
in different blocks or at multiple locations, we develop a distributed
subsampling framework, in which statistics are computed simultaneously on
smaller partitions of the full data. Asymptotic properties of the resultant
aggregated estimator are investigated. We illustrate and evaluate the proposed
strategies through numerical experiments on simulated and real data sets.
