Approximation by Penultimate Stable Laws

• Autorzy: de Haan L. , Peng L. , Pereira H. I.
• Języki publikacji: EN

Abstrakty

EN

In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices α_n → 2 than by a normal distribution. We discuss when this happens and how much the convergencerate can be improved by using penultimate approximations. Similar results are valid for other stable distributions.

Słowa kluczowe

EN

random variables; stable distributions; penultimate approximations

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 105--121
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

de Haan L.

• Erasmus University Rotterdam, 300 Rotterdam, P.O. Box 1738, The Netherlands

autor

Peng L.

• Erasmus University Rotterdam, 300 Rotterdam, P.O. Box 1738, The Netherlands

autor

Pereira H. I.

• University of Lisbon, R. Ernesto Vasconcelos C 1700, Lisbon, Portugal

Bibliografia

• [1] N. Bingham, C. Goldie and J. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1987.
• [2] H. Drees, On smooth statistical tail functionals, Scand. J. Statist. 25 (1) (1998), pp. 187-210.
• [3] J. Geluk and L. de Haan, Regular Variation, Extensions and Tauberian Theorems, CWI Tract 40, Amsterdam 1987.
• [4] L. de Haan and L. Peng, Exact rates of convergence to a stable law, J. London Math. Soc. (1996).
• [5] - Slow convergence to normality: an Edgeworth expansion without third moment, Probab. Math. Statist. 17 (2) (1997), pp. 395-406.
• [6] L. de Haan and T. T. Pereira, Estimating the index of a stable distribution, Statist. Probab. Lett. 41 (1999), pp. 39-55.
• [7] L. de Haan and U. Stadtmüller, Generalized regular variation of second order, J. Austral. Math. Soc. Ser. A 61 (1996), pp. 381-395.
• [8] O. Oliveira, Attraction coefficients and convergence rate in pre-asymptotic situations (in Portuguese), in: R. Vasconcelos et al. (Eds.), A estatistica a decifrar o mundo, Edições salamandra, Lisbon 1996.
• [9] E. Omey and E. Willekens, Π-variation with remainder, J. London Math. Soc. 37 (1988), pp. 105-118.
• [10] H. Iglesias Pereira, O. Oliveira and D. Pestana, Stable limits and pre-asymptotic behaviour (in Portuguese), R. Vasconcelos et al. (Eds.), A estatistica a decifrar o mundo, Edições salamandra, Lisbon 1996.