  Nearest neighbor is a popular nonparametric method for classification and
regression with many appealing properties. In the big data era, the sheer
volume and spatial/temporal disparity of big data may prohibit centrally
processing and storing the data. This has imposed considerable hurdle for
nearest neighbor predictions since the entire training data must be memorized.
One effective way to overcome this issue is the distributed learning framework.
Through majority voting, the distributed nearest neighbor classifier achieves
the same rate of convergence as its oracle version in terms of both the regret
and instability, up to a multiplicative constant that depends solely on the
data dimension. The multiplicative difference can be eliminated by replacing
majority voting with the weighted voting scheme. In addition, we provide sharp
theoretical upper bounds of the number of subsamples in order for the
distributed nearest neighbor classifier to reach the optimal convergence rate.
It is interesting to note that the weighted voting scheme allows a larger
number of subsamples than the majority voting one. Our findings are supported
by numerical studies using both simulated and real data sets.
