Estimation of misclassification rate in the Asymptotic Rare and Weak model with sub-Gaussian noises
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Published:2023-01-12
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Volume:
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ISSN:0219-6913
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Container-title:International Journal of Wavelets, Multiresolution and Information Processing
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language:en
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Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.
Author:
Liu Youming1,
Zhang Zhentao1ORCID
Affiliation:
1. Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, P. R. China
Abstract
Motivated by Jin–Ke–Wang’s work (J. Jin, Z. T. Ke and W. Wang, Ann. Statist. 45(5) (2017) 2151–2189), this paper studies estimation of misclassification rate in the Asymptotic Rare and Weak (ARW) model. In contrast to Jin–Ke–Wang’s theorem, we measure the performance of the estimator by the misclassification rate instead of Hamming distance, and extend the Gaussian noise to sub-Gaussian’s. The probability estimation with convergence rate is first given under some conditions. Then we prove that condition necessary as well. A direct corollary of our estimation can be compared with Jin–Ke–Wang’s theorem. It turns out that our statistical limit coincides with theirs.
Funder
Natural Science Foundation of Jilin Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Information Systems,Signal Processing