Geodesic
Properties of Hill's estimator of extreme value index for impure samples
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2014), pp. 3-6 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider the consistency and asymptotic normality of the Hill estimator of the extreme value index for a sample from the sequence of independent and identically distributed random variables with asymptotically increasing additive pollution. In addition, the cases when the statistical construction of the estimator is possible are analyzed. 
@article{VMUMM_2014_1_a0,
     author = {I. V. Rodionov},
     title = {Properties of {Hill's} estimator of extreme value index for impure samples},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--6},
     year = {2014},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_1_a0/}
}
TY  - JOUR
AU  - I. V. Rodionov
TI  - Properties of Hill's estimator of extreme value index for impure samples
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2014
SP  - 3
EP  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2014_1_a0/
LA  - ru
ID  - VMUMM_2014_1_a0
ER  - 
%0 Journal Article
%A I. V. Rodionov
%T Properties of Hill's estimator of extreme value index for impure samples
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2014
%P 3-6
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2014_1_a0/
%G ru
%F VMUMM_2014_1_a0
I. V. Rodionov. Properties of Hill's estimator of extreme value index for impure samples. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2014), pp. 3-6. http://geodesic.mathdoc.fr/item/VMUMM_2014_1_a0/

[1] Fereira A., Haan L. de, Extreme value theory. An introduction, Springer Series in Operations Research and Financial Engineering, Springer, N.Y., 2006 | MR

[2] Hill B.M., “A simple general approach to inference about the tail of a distribution”, Ann. Statist., 3 (1975), 1163–1174 | DOI | MR | Zbl

[3] Fisher R.A., Tippet L.H.C., “Limiting forms of the frequency distribution of the largest or smallest member of a sample”, Proc. Cambridge Phil. Soc., 24 (1928), 180–190 | DOI | Zbl

[4] Leadbetter M.R., Lingren G., Rootzén H., Extreme and related properties of random sequences and processes, Springer Statistics Series, Springer, Berlin–Heidelberg–N.Y., 1983 | DOI | MR

[5] Kuznetsov D.S., “Predelnye teoremy dlya maksimuma sluchainykh velichin”, Vestn. Mosk. un-ta. Matem. Mekhan., 2005, no. 3, 6–9

[6] Olshanskii K.A., “Ob ekstremalnom indekse prorezhennogo protsessa avtoregressii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2004, no. 3, 17–23

[7] Kudrov A.V., Piterbarg V.I., “On maxima of partial samples in Gaussian sequences with pseudo-stationary trends”, Liet. matem. rink., 47:1 (2007), 1–10 | MR

[8] Rodionov I.V., “Puassonovskaya predelnaya teorema dlya vysokikh ekstremumov vremennogo ryada s sezonnoi sostavlyayuschei i strogo monotonnym trendom”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 1, 12–17 | Zbl

[9] Billingsley P., Convergence of probability measures, Wiley, N.Y., 1968 | MR | Zbl