Geodesic
Asymptotic behavior of statistical estimates for samples with a discon­tinuous density
Sbornik. Mathematics, Tome 16 (1972) no. 4, pp. 573-606 
I. A. Ibragimov; R. Z. Khas'minskii. Asymptotic behavior of statistical estimates for samples with a discon­tinuous density. Sbornik. Mathematics, Tome 16 (1972) no. 4, pp. 573-606. http://geodesic.mathdoc.fr/item/SM_1972_16_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the authors study the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind. Bibliography: 9 titles.

[1] H. Chernoff, H. Rubin, The estimation of the location of a discontinuity in density, Proc. 3d Berkeley Symp. Math. Stat. and Prob., Univ. Calif. Press, 1956 | MR

[2] H. Rubin, “The estimation of discontinuities in multivariate densities and related problems in stochastic processes”, Proc. of the fourth Berkeley Symp. on Prob. Theory and Statistics, v. 1, 1961, 563–574 | MR | Zbl

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[4] I. A. Ibragimov, R. Z. Khasminskii, “Ob asimptoticheskom povedenii obobschennykh baiesovskikh otsenok”, DAN SSSR, 194:2 (1970), 267–260

[5] I. A. Ibragimov, R. 3. Khasminskii, “Asimptoticheskoe povedenie nekotorykh statisticheskikh otsenok. I, II”, Teor. veroyatnostei, 17:3 (1972), 469–486 ; Теор. вероятностей, 18:1 (1973), 78–93 | MR | Zbl | MR | Zbl

[6] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Nauka, Moskva, 1965 | MR | Zbl

[7] M. Loev, Teoriya veroyatnostei, IL, Moskva, 1962 | MR

[8] A. M. Kagan, “Teoriya otsenivaniya dlya semeistv s parametrami sdviga, masshtaba i eksponentnykh”, Trudy matem. in-ta im. V. A. Steklova, CIV (1968), 19–87 | MR

[9] S. R. Rao, Lineinye statisticheskie metody i ikh primeneniya, Nauka, Moskva, 1968 | MR | Zbl