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

DOI:
https://doi.org/10.1090/S0094-9000-07-00696-5

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 for smooth distributions, while the rate of convergence of the Bayes empirical estimators is of order where 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

Email:
ivanko@lemma-insur.com.ua

**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

Email:
mre@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-07-00696-5

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