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MER-ESTIMATOR OF MULTIDIMENSIONAL BAYESIAN THRESHOLD IN TWO-CLASS CLASSIFICATION PROBLEM
Keywords:
estimator, multidimensional Bayesian threshold, mixture with varying concentrations.DOI:
https://doi.org/10.17654/0972361722074Abstract
Some threshold-based classification rules in case of two classes are defined. In assumption, that a learning sample is obtained from a mixture with varying concentration, the MER-estimator of multidimensional Bayesian threshold is constructed. The conditions of convergence in probability of estimator are found.
Received: August 1, 2022
Revised: September 27, 2022
Accepted: October 5, 2022
References
R. E. Maiboroda, Estimates for distributions of components of mixtures with varying concentrations, Ukrainian Math. J. 48(4) (1996), 618-622.
R. E. Maiboroda, An asymptotically efficient probability estimator constructed from observations of a mixture, Theory Probab. Math. Statist. 59 (1999), 121-128.
R. E. Maiboroda, Projective estimates for changing concentrations of mixtures, Theory Probab. Math. Statist. 46 (1993), 71-75.
O. V. Sugakova, Asymptotics of a kernel estimate for distribution density constructed from observations of a mixture with varying concentration, Theory Probab. Math. Statist. 59 (1999), 161-171.
Yu. O. Ivan’ko, Asymptotics of kernel estimations of densities and their derivatives constructed from observations of mixtures with varying concentrations, Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 9 (2003), 29-35.
O. Kubaychuk, Fast correction algorithms for weighted empirical distribution functions, Advances and Applications in Statistics 54(2) (2019), 315-326.
http://dx.doi.org/10.17654/AS054020315.
C. J. Stone, Consistent nonparametric regression, Ann. Statist. 5(4) (1977), 595-620.
H. Teicher, Identifiability of mixtures, Ann. Math. Statist. 31(1) (1961), 244-248.
S. A. Yakovitz and J. Spragins, On the identifiability of finite mixtures, Ann. Math. Statist. 39(1) (1968), 209-214.
P. Hall and X.-H. Zhou, Nonparametric estimation of component distributions in a multivariate mixture, Ann. Statist. 31(1) (2003), 201-224.
R. E. Maiboroda and O. V. Sugakova, Estimating and classification by observations from the mixture (“Kyiv University”, Kyiv, 2008) (Ukrainian).
Yu. O. Ivan’ko and R. E. Maiboroda, The asymptotic behavior of threshold-based classification rules constructed from a sample from a mixture with varying concentrations, Theory Probab. Math. Statist. 74 (2007), 37-47.
O. Kubajchuk, The asymptotics of the estimator of the Bayesian border, (Ukrainian, English summary), Visn., Mat. Mekh., Kyiv. Univ. Im. Tarasa Shevchenka 19 (2008), 47-51.
O. O. Kubaychuk, The estimator asymptotic behavior of the empirical risk minimization method for Bayesian border, (Ukrainian English summary), Research Bulletin of the NTU of Ukraine, Kyiv Politechnic Institute 4 (2010), 78-85.
O. Kubaychuk, The asymptotic behavior of threshold-based classification rules in case of three classes, J. Adv. Math. 12(5) (2016), 6261-6269.
https://doi.org/10.24297/jam.v12i5.318.
O. Kubaychuk, EBC-estimator of multidimensional Bayesian threshold in case of two classes, Journal of Statistical Theory and Applications 19(3) (2020), 342-351. https://dx.doi.org/10.2991/jsta.d.200824.001.
R. E. Maiboroda, Statistical Analysis of Mixtures. A Course of Lectures (“Kyiv University”, Kyiv, 2003) (Ukrainian).
Yu. O. Ivan’ko, The asymptotic behavior of kernel estimators and their derivatives constructed from observations from a mixture with varying concentrations, Visnyk KNU, Ser. Matematika Mekhanika 9 (2003), 29-35.
O. V. Sugakova, Asymptotics of a kernel estimate for distribution density constructed from observations of a mixture with varying concentrations, Theory Probab. Math. Statist. 59 (1999), 161-171.
O. Kubaychuk, Estimation of moments by observations from mixtures with varying concentrations, Theory of Stochastic Processes 8(24) (2002), 226-231.
O. O. Kubajchuk, Estimation of moments by observation from mixtures using the corrected weighted empirical distribution functions, Visn., Mat. Mekh., Kyiv. Univ. Im. Tarasa Shevchenka 9 (2003), 48-52.
R. Maiboroda and O. Kubaichuk, Asymptotic normality of improved weighted empirical distribution functions, Theory Probab. Math. Statist. 69 (2004), 95-102.
R. Maiboroda and O. Kubaichuk, Improved estimators for moments constructed from observations of a mixture, Theory Probab. Math. Statist. 70 (2005), 83-92.
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