Geodesic
Lower bounds to the accuracy of sample maximum estimation
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 156-161.

Voir la notice de l'article provenant de la source Math-Net.Ru

We derive lower bounds for sup-norm losses of estimators of the distribution function of a sample maximum, and show that their consistent estimation in a general situation is impossible.
Keywords: Sample maximum, lower bounds.
Mots-clés : consistent estimation 
@article{THSP_2009_15_2_a10,
     author = {S. Y. Novak},
     title = {Lower bounds to the accuracy of sample maximum estimation},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {156--161},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a10/}
}
TY  - JOUR
AU  - S. Y. Novak
TI  - Lower bounds to the accuracy of sample maximum estimation
JO  - Teoriâ slučajnyh processov
PY  - 2009
SP  - 156
EP  - 161
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a10/
LA  - en
ID  - THSP_2009_15_2_a10
ER  - 
%0 Journal Article
%A S. Y. Novak
%T Lower bounds to the accuracy of sample maximum estimation
%J Teoriâ slučajnyh processov
%D 2009
%P 156-161
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a10/
%G en
%F THSP_2009_15_2_a10
S. Y. Novak. Lower bounds to the accuracy of sample maximum estimation. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 156-161. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a10/

[1] K. B. Athreya, J. Fukuchi, “Bootstrapping extremes of i.i.d. random variables”, NIST Special Publication 866, Proc. Conf. Extreme Value Theory Appl., v. 3, eds. J. Galambos, J. Lechner, E. Simiu, 1994

[2] K. B. Athreya, J. Fukuchi, S. N. Lahiri, “On the bootstrap and the moving block bootstrap for the maximum of a stationary process”, J. Statist. Plan. Infer., 76 (1999), 1–17

[3] J. Beirlant, L. Devroye, “On the impossibility of estimating densities in the extreme tail”, Statist. Probab. Letters, 43:1 (1999), 57–64

[4] P. Embrechts, C. Küppelberg, T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997

[5] W. Feller, An introduction to probability theory and its applications, Wiley, New York, 1971

[6] J. Galambos, The asymptotic theory of extreme order statistics, Krieger, Melbourne, 1987

[7] B. V. Gnedenko, “Sur la distribution du terme maximum d'une série aléatoire”, Ann. Math., 44 (1943)

[8] M. R. Leadbetter, G. Lindgren, H. Rootzén, Extremes and related properties of random sequences and processes, Springer, New York, 1983

[9] S. Y. Novak, “Generalized kernel density estimator”, Theory Probab. Appl., 44:3 (1999), 634–645

[10] S. Y. Novak, “Inference on heavy tails from dependent data”, Siberian Adv. Math., 12:2 (2002), 73–96

[11] S. Y. Novak, “Advances in Extreme Value Theory with Applications to Finance”, New Business and Finance Research Developments, Nova Science, New York, 2009, 199–251

[12] S. Y. Novak, “On impossibility of consistent estimation of the distribution function of a sample maximum”, Statistics, 2009 (to appear)

[13] G. L. O'Brien, “Extreme values for stationary and Markov sequences”, Ann. Probab., 15:1 (1987), 281–291

[14] R. E. Paley, A. Zygmund, “A note on analytic functions in the unit circle”, Proc. Camb. Phil. Soc., 28 (1932), 266–272

[15] J. Pfanzagl, “On local uniformity for estimators and confidence limits”, J. Statist. Plann. Inference, 84 (2000), 27–53