Optimal Nonparametric Inference under Quantization

Statistical inference based on lossy or incomplete samples is of fundamental importance in research areas such as signal/image processing, medical image storage, remote sensing, signal transmission. In this paper, we propose a nonparametric testing procedure based on quantized samples. In contrast to the classic nonparametric approach, our method lives on a coarse grid of sample information and are simple-to-use. Under mild technical conditions, we establish the asymptotic properties of the proposed procedures including asymptotic null distribution of the quantization test statistic as well as its minimax power optimality. Concrete quantizers are constructed for achieving the minimax optimality in practical use. Simulation results and a real data analysis are provided to demonstrate the validity and effectiveness of the proposed test. Our work bridges the classical nonparametric inference to modern lossy data setting.