Informatics and Applications
2024, Volume 18, Issue 3, pp 69-79
ASYMPTOTIC NORMALITY AND STRONG CONSISTENCY OF RISK ESTIMATE WHEN USING THE FDR THRESHOLD UNDER WEAK DEPENDENCE CONDITION
- M. O. Vorontsov
- O. V. Shestakov
Abstract
An approach to solving the problem of noise removal in a large array of sparse data is considered based
on the method of controlling the average proportion of false hypothesis rejections (False Discovery Rate, FDR).
This approach is equivalent to threshold processing procedures that remove array components whose values do not
exceed some specified threshold. The observations in the model are considered weakly dependent. To control the degree of dependence, restrictions on the strong mixing coefficient and the maximum correlation coefficient are
used. The mean-square risk is used as a measure of the effectiveness of the considered approach. It is possible
to calculate the risk value only on the test data; therefore, its statistical estimate is considered in the work and its
properties are investigated. The asymptotic normality and strong consistency of the risk estimate are proved when
using the FDR threshold under conditions of weak dependence in the data.
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[+] About this article
Title
ASYMPTOTIC NORMALITY AND STRONG CONSISTENCY OF RISK ESTIMATE WHEN USING THE FDR THRESHOLD UNDER WEAK DEPENDENCE CONDITION
Journal
Informatics and Applications
2024, Volume 18, Issue 3, pp 69-79
Cover Date
2024-09-20
DOI
10.14357/19922264240309
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
thresholding; multiple hypothesis testing; risk estimate
Authors
M.O. Vorontsov  ,  and O. V. Shestakov , , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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