Empirical Bayesian classification for observations with admixture
Author:
O. Sugakova
Translated by:
O. I. Klesov
Journal:
Theor. Probability and Math. Statist. 84 (2012), 165-172
MSC (2010):
Primary 62G05; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-2012-00858-2
Published electronically:
August 2, 2012
MathSciNet review:
2857426
Full-text PDF Free Access
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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.
References
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- R. E. Maĭboroda and O. V. Sugakova, Estimation and classification after observations in a mixture, Kyiv University, Kyiv, 2008. (Ukrainian)
- 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, DOI https://doi.org/10.1090/S0094-9000-2010-00801-5
- O. Sugakova, Density estimation by observations with admixture, Theory Stoch. Process. 16 (2010), no. 1, 103–110. MR 2779834
- A. A. Borovkov, Matematicheskaya statistika, “Nauka”, Moscow, 1984 (Russian). Otsenka parametrov. Proverka gipotez. [Estimation of parameters. Testing of hypotheses]. MR 782295
- Jun Shao, Mathematical statistics, 2nd ed., Springer Texts in Statistics, Springer-Verlag, New York, 2003. MR 2002723
References
- L. Bordes, P. Delmas, and P. Vandekerkhove, Semiparametric estimation of a two-component mixture model where one component is known, Scand. J. Statist. 33 (2006), 733–752. MR 2300913 (2008f:62049)
- R. E. Maĭboroda and O. V. Sugakova, Estimation and classification after observations in a mixture, Kyiv University, Kyiv, 2008. (Ukrainian)
- O. Sugakova, An estimator of the location parameter obtained from observations with admixture, Teor. Imovir. Matem. Statist. 80 (2009), 128–137; English transl. in Theory Probability and Math. Statist. 80 (2010), 143–152. MR 2541959 (2010e:62077)
- O. Sugakova, Density estimation by observation with admixture, Theory Stoch. Process. 16 (32) (2010), no. 1, 103–110. MR 2779834 (2012a:62116)
- A. A. Borovkov, Mathematical Statistics, Nauka, Moscow, 1977; English transl. Gordon and Breach Science Publishers, Amsterdam, 1998. MR 782295 (86i:62001)
- J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998. MR 2002723 (2004g:62002)
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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
Received by editor(s):
June 21, 2010
Published electronically:
August 2, 2012
Article copyright:
© Copyright 2012
American Mathematical Society
