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Theory of Probability and Mathematical Statistics

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The asymptotic behavior of threshold-based classification rules constructed from a sample from a mixture with varying concentrations

Authors: Yu. Ivan'ko and R. Maiboroda
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 37-47
MSC (2000): Primary 62H30; Secondary 62G07
Published electronically: June 25, 2007
MathSciNet review: 2336777
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a problem on finding the best threshold-based classification rule constructed from a sample from a mixture with varying concentrations. We show that the rate of convergence of the minimal empirical risk estimators to the optimal threshold is of order $ N^{-1/3}$ for smooth distributions, while the rate of convergence of the Bayes empirical estimators is of order $ N^{-2/5}$ where $ N$ is the size of a sample.

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Additional Information

Yu. Ivan'ko
Affiliation: SK Lemma-Vite, Brats’ka Street, Kyiv, 6, 04070 Ukraine

R. Maiboroda
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Glushkov Avenue, 6, Kyiv, 03127, Ukraine

Keywords: Minimization of the empirical risk, kernel estimators of densities, Bayes empirical classification rule, estimates of components of a mixture, mixtures with varying concentrations
Received by editor(s): December 20, 2004
Published electronically: June 25, 2007
Article copyright: © Copyright 2007 American Mathematical Society