  Large-scale rare events data are commonly encountered in practice. To tackle
the massive rare events data, we propose a novel distributed estimation method
for logistic regression in a distributed system. For a distributed framework,
we face the following two challenges. The first challenge is how to distribute
the data. In this regard, two different distribution strategies (i.e., the
RANDOM strategy and the COPY strategy) are investigated. The second challenge
is how to select an appropriate type of objective function so that the best
asymptotic efficiency can be achieved. Then, the under-sampled (US) and inverse
probability weighted (IPW) types of objective functions are considered. Our
results suggest that the COPY strategy together with the IPW objective function
is the best solution for distributed logistic regression with rare events. The
finite sample performance of the distributed methods is demonstrated by
simulation studies and a real-world Sweden Traffic Sign dataset.
