On the accuracy of inference on heavy-tailed distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 3, pp. 598-607 Cet article a éte moissonné depuis la source Math-Net.Ru

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S. Yu. Novak. On the accuracy of inference on heavy-tailed distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 3, pp. 598-607. http://geodesic.mathdoc.fr/item/TVP_2013_58_3_a10/

[1] Beirlant J., Bouquiaux C., Werker B. J. M., “Semiparametric lower bounds for tail index estimation”, J. Statist. Plann. Inference, 136:3 (2006), 705–729 | DOI | MR | Zbl

[2] Devroye L., “Another proof of a slow convergence result of Birgé”, Statist. Probab. Lett., 23:1 (1995), 63–67 | DOI | MR | Zbl

[3] Donoho D. L., Liu R. C., “Geometrizing rates of convergence. II; III”, Ann. Statist., 19:2 (1991), 633–667 ; 668–701 | DOI | MR | Zbl | Zbl

[4] Drees H., “Minimax risk bounds in extreme values theory”, Ann. Statist., 29:1 (2001), 266–294 | DOI | MR | Zbl

[5] Fama E. F., Roll R., “Some properties of symmetric stable distributions”, J. Amer. Statist. Assoc., 63 (1968), 817–836 | DOI | MR

[6] Farrell R. H., “On the best obtainable asymptotic rates of convergence in estimation of a density function at a point”, Ann. Math. Statist., 43 (1972), 170–180 | DOI | MR | Zbl

[7] Hall P., “On estimating the endpoint of a distribution”, Ann. Statist., 10:2 (1982), 556–568 | DOI | MR | Zbl

[8] Hall P., Welsh A. H., “Best attainable rates of convergence for estimates of parameters of regular variation”, Ann. Statist., 12:3 (1984), 1079–1084 | DOI | MR | Zbl

[9] Huber C., “Lower bounds for function estimation”, Festschrift for L. Le Cam, Springer, New York, 1997, 245–258 | DOI | MR | Zbl

[10] Embrechts P., Klüppelberg C., Mikosch T., Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin, 1997, 645 pp. | MR | Zbl

[11] Goldie C. M., Smith R. L., “Slow variation with remainder: theory and applications”, Quart. J. Math. Oxford, 38:149 (1987), 45–71 | DOI | MR | Zbl

[12] Ibragimov I. A., Khasminskii R. Z., “Ob otsenke plotnosti raspredeleniya”, Zap. nauch. sem. LOMI, 98, 1980, 61–85 | MR | Zbl

[13] Ibragimov I. A., Khasminskii R. Z., Asimptoticheskaya teoriya otsenivaniya, Nauka, M., 1979, 527 pp. | MR

[14] Lenstra A. J., “Cramér–Rao revisited”, Bernoulli, 11:2 (2005), 263–282 | DOI | MR | Zbl

[15] Mandelbrot B. B., “New methods in statistical economics”, J. Political Economy, 71 (1963), 421–440 | DOI

[16] Novak S. Yu., Utev S. A., “Ob asimptotike raspredeleniya otnosheniya summ sluchainykh velichin”, Cib. matem. zhurn., 31 (1990), 92–101 | MR

[17] Novak S. Yu., “O raspredelenii otnosheniya summ sluchainykh velichin”, Teoriya veroyatn. i ee primen., 41:3 (1996), 533–560 | DOI | MR | Zbl

[18] Novak S. Y., “Advances in extreme value theory with applications to finance”, New Business and Finance Research Developments, ed. C. Keene, Nova Science, New York, 2009, 199–251 | Zbl

[19] Pfanzagl J., “On local uniformity for estimators and confidence limits”, J. Statist. Plann. Inference, 84:1–2 (2000), 27–53 | DOI | MR | Zbl

[20] Resnick S. I., “Heavy tail modeling and teletraffic data”, Ann. Statist., 25:5 (1997), 1805–1869 | DOI | MR | Zbl

[21] Shemyakin A. E., “Ob informatsionnykh neravenstvakh v teorii parametricheskogo otsenivaniya”, Teoriya veroyatn. i ee primen., 37:3 (1992), 121–123 | MR | Zbl

[22] Tsybakov A. B., Introduction to Nonparametric Estimation, Springer, New York, 2009, 175 pp. | MR | Zbl