Nonparametric Inference under B-bits Quantization
This work addresses the need for reliable inference in fields like signal processing and medical imaging where data is often lossy or quantized, representing an incremental advancement in nonparametric methods.
The paper tackles the problem of statistical inference from data quantized to B bits, proposing a nonparametric testing procedure that achieves the classical minimax rate of testing when B exceeds a threshold, as validated by simulations and real-data analysis.
Statistical inference based on lossy or incomplete samples is often needed 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 samples quantized to $B$ bits through a computationally efficient algorithm. Under mild technical conditions, we establish the asymptotic properties of the proposed test statistic and investigate how the testing power changes as $B$ increases. In particular, we show that if $B$ exceeds a certain threshold, the proposed nonparametric testing procedure achieves the classical minimax rate of testing (Shang and Cheng, 2015) for spline models. We further extend our theoretical investigations to a nonparametric linearity test and an adaptive nonparametric test, expanding the applicability of the proposed methods. Extensive simulation studies {together with a real-data analysis} are used to demonstrate the validity and effectiveness of the proposed tests.