Empirical Bayesian classification for observations with admixture

Author:
O. Sugakova

Translated by:
O. I. Klesov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **84** (2011).

Journal:
Theor. Probability and Math. Statist. **84** (2012), 165-172

MSC (2010):
Primary 62G05; Secondary 62G20

Published electronically:
August 2, 2012

MathSciNet review:
2857426

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of classification of an object by using observations after a numerical characteristic under the assumption that each object belongs to one of the two given classes. The distribution of the characteristic is unknown for objects of the first class but is assumed to be symmetric. The distribution for the second class is known. We construct an empirical Bayesian classifier and prove a result concerning the asymptotic behavior of the error probability.

**1.**Laurent Bordes, Céline Delmas, and Pierre Vandekerkhove,*Semiparametric estimation of a two-component mixture model where one component is known*, Scand. J. Statist.**33**(2006), no. 4, 733–752. MR**2300913**, 10.1111/j.1467-9469.2006.00515.x**2.**R. E. Maĭboroda and O. V. Sugakova,*Estimation and classification after observations in a mixture*, Kyiv University, Kyiv, 2008. (Ukrainian)**3.**O. Sugakova,*Estimation of the mean from observations with an admixture*, Teor. Ĭmovīr. Mat. Stat.**80**(2009), 128–137 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist.**80**(2010), 143–152. MR**2541959**, 10.1090/S0094-9000-2010-00801-5**4.**O. Sugakova,*Density estimation by observations with admixture*, Theory Stoch. Process.**16**(2010), no. 1, 103–110. MR**2779834****5.**A. A. Borovkov,*Matematicheskaya statistika*, “Nauka”, Moscow, 1984 (Russian). Otsenka parametrov. Proverka gipotez. [Estimation of parameters. Testing of hypotheses]. MR**782295****6.**Jun Shao,*Mathematical statistics*, 2nd ed., Springer Texts in Statistics, Springer-Verlag, New York, 2003. MR**2002723**

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Additional Information

**O. Sugakova**

Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kyiv 03127, Ukraine

Email:
sugak@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-2012-00858-2

Received by editor(s):
June 21, 2010

Published electronically:
August 2, 2012

Article copyright:
© Copyright 2012
American Mathematical Society