Nonparametric Inference under B-bits Quantization

• URL: http://arxiv.org/abs/1901.08571v3
• Date: Fri, 11 Aug 2023 15:17:35 GMT
• Title: Nonparametric Inference under B-bits Quantization
• Authors: Kexuan Li, Ruiqi Liu, Ganggang Xu, Zuofeng Shang
• Abstract summary: We propose a nonparametric testing procedure based on samples quantized to $B$ bits. In particular, we show that if $B$ exceeds a certain threshold, the proposed nonparametric testing procedure achieves the classical minimax rate of testing.
• Score: 5.958064620718292
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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