  In massive data analysis, training and testing data often come from very
different sources, and their probability distributions are not necessarily
identical. A feature example is nonparametric classification in posterior drift
model where the conditional distributions of the label given the covariates are
possibly different. In this paper, we derive minimax rate of the excess risk
for nonparametric classification in posterior drift model in the setting that
both training and testing data have smooth distributions, extending a recent
work by Cai and Wei (2019) who only impose smoothness condition on the
distribution of testing data. The minimax rate demonstrates a phase transition
characterized by the mutual relationship between the smoothness orders of the
training and testing data distributions. We also propose a computationally
efficient and data-driven nearest neighbor classifier which achieves the
minimax excess risk (up to a logarithm factor). Simulation studies and a
real-world application are conducted to demonstrate our approach.
