When data is of an extraordinarily large size or physically stored in
different locations, the distributed nearest neighbor (NN) classifier is an
attractive tool for classification. We propose a novel distributed adaptive NN
classifier for which the number of nearest neighbors is a tuning parameter
stochastically chosen by a data-driven criterion. An early stopping rule is
proposed when searching for the optimal tuning parameter, which not only speeds
up the computation but also improves the finite sample performance of the
proposed Algorithm. Convergence rate of excess risk of the distributed adaptive
NN classifier is investigated under various sub-sample size compositions. In
particular, we show that when the sub-sample sizes are sufficiently large, the
proposed classifier achieves the nearly optimal convergence rate. Effectiveness
of the proposed approach is demonstrated through simulation studies as well as
an empirical application to a real-world dataset