  Distributed systems have been widely used in practice to accomplish data
analysis tasks of huge scales. In this work, we target on the estimation
problem of generalized linear models on a distributed system with nonrandomly
distributed data. We develop a Pseudo-Newton-Raphson algorithm for efficient
estimation. In this algorithm, we first obtain a pilot estimator based on a
small random sample collected from different Workers. Then conduct one-step
updating based on the computed derivatives of log-likelihood functions in each
Worker at the pilot estimator. The final one-step estimator is proved to be
statistically efficient as the global estimator, even with nonrandomly
distributed data. In addition, it is computationally efficient, in terms of
both communication cost and storage usage. Based on the one-step estimator, we
also develop a likelihood ratio test for hypothesis testing. The theoretical
properties of the one-step estimator and the corresponding likelihood ratio
test are investigated. The finite sample performances are assessed through
simulations. Finally, an American Airline dataset is analyzed on a Spark
cluster for illustration purpose.
