Geodesic
Empirical estimates with minimal $d$-risk for discrete exponential families
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 89-98.

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We develop a $d$-posteriori approach to estimations with uniformly minimal $d$-risk, when the a priori distribution is completely unknown. For a scalar parameter of a discrete exponential family we construct empirical estimates based on archive data and prove the convergence of the empirical $d$-risk to the true one. As an example we adduce the estimation of the Poisson distribution parameter. We numerically study the accuracy of the estimates by the statistical modeling method.
Keywords: empirical $d$-posteriori approach, estimates with uniformly minimal $d$-risk, convergence of empirical $d$-risk, discrete exponential families. 
@article{IVM_2010_8_a9,
     author = {E. D. Sherman},
     title = {Empirical estimates with minimal $d$-risk for discrete exponential families},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {89--98},
     publisher = {mathdoc},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_8_a9/}
}
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E. D. Sherman. Empirical estimates with minimal $d$-risk for discrete exponential families. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 89-98. http://geodesic.mathdoc.fr/item/IVM_2010_8_a9/

[1] Simushkin S. V., Volodin I. N., “Statistical inference with a minimal $d$-risk”, Lect. Note in Math., 1021, 1983, 107–114 | MR

[2] Volodin I. N., Simushkin S. V., “Statisticheskie vyvody s minimalnym $d$-riskom”, Issledovaniya po priklad. matem., 11, Izd-vo KGU, Kazan, 1984, 25–39 | MR

[3] Volodin I. N., Simushkin S. V., “Nesmeschennost i baiesovost”, Izv. vuzov. Matematika, 1987, no. 1, 3–7 | MR

[4] Volodin I. N., Novikov A. N., “Statisticheskie otsenki s asimptoticheski minimalnym $d$-riskom”, Teoriya veroyat. i ee primenen., 38:1 (1993), 20–32 | MR | Zbl

[5] Volodin I. N., Novikov A. N., Simushkin S. V., “Garantiinyi statisticheskii kontrol kachestva: aposteriornyi podkhod”, Obozrenie priklad. i promysh. matemat., 1:2 (1994), 1–32

[6] Simushkin S. V., “Empiricheskii $d$-aposteriornyi podkhod k probleme garantiinosti statisticheskogo vyvoda”, Izv. vuzov. Matematika, 1983, no. 11, 42–58 | MR | Zbl

[7] Robbins H., “An empirical Bayes approach to statistic”, Proc. Third Berkeley Symp. Math. Statist. Probab., v. 1, Univ. of Calif. Press, 1955, 157–164 | MR

[8] van der Vaart A. W., Asymptotic statistics, Cambridge University Press, Cambridge, 1998 | MR

[9] Fedoryuk M. V., Asimptotika: integraly i ryady, Nauka, M., 1987 | MR | Zbl