Title: Optimal Nonparametric Inference under Quantization,
Abstract: 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.