We consider the problem of construction of point and interval estimators for the Bayesian risk of a group classification decision rule provided that the elements of training samples have distributions belonging to the same one-parameter exponential family. We propose a solution to this problem using the asymptotic normality and efficiency of an unbiased risk estimator. An example of application of the obtained theoretical results is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. A. Abusev and Ya. P. Lumelsky, Statistical Group Classification, Perm University Press, Perm (1987).
S.A. Ayvasian, V.M. Buchstaber, I. S. Yenjukov, and L.D. Meshalkin, Applied Statistics: Classification and Reduction of Dimensionality, Finansy i Statistika, Moscow (1989).
E. V.Babushkina and V. V.Chichagov, “Interval estimation of group classification risk with the use of unbiased estimates,” in: Abstracts of 12th All-Russian Conference “Mathematical Methods of Image Recognition-12,” Moscow (2005), pp. 22–25.
V. V. Ivshin and Ya. P. Lumelsky, Statistical Problems of Estimation in the “Load–Durability” Model, Perm University Press, Perm (1995).
M. A. Oleynik and V. V. Chichagov, “Interval estimation of probability P(X < Y) in case of oneparameter exponential families using unbiased estimate,” J. Math. Sci., 205, No. 1, 45–54 (2015).
V. G. Voinov and M.C. Nikulin, Unbiased Estimates and Their Applications, Nauka, Moscow (1989).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 4–11, 2006
Rights and permissions
About this article
Cite this article
Babushkina, E.V., Chichagov, V. Application of Unbiased Estimators to Group Classification Risk Estimation. J Math Sci 228, 475–480 (2018). https://doi.org/10.1007/s10958-017-3636-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3636-5