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The asymptotic behavior of threshold-based classification rules constructed from a sample from a mixture with varying concentrations
Author(s):
Yu.
Ivan'ko;
R.
Maiboroda
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 74
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 74
(2007),
37-47.
MSC (2000):
Primary 62H30;
Secondary 62G07
Posted:
June 25, 2007
Retrieve article in:
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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.
References:
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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:
10.1090/S0094-9000-07-00696-5
PII:
S 0094-9000(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):
20/DEC/2004
Posted:
June 25, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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