Edgeworth expansions for L-statistics

• Autorzy: Alberink B. , Pap G. , van Zuijlen M. C. A.
• Języki publikacji: EN

Abstrakty

EN

We study the approximation by a short Edgeworth expansion of the distribution function of normalized linear combinations [formula] of order statistics of n independent random variables with common distribution function F. Under the assumptions [formula] for some p₁, q₁, r₁ ∈ R p₂, q₂, r₂, C≥0, к ∈ [0.5/4) with an appropriate balance in these parameters, and under additional moment conditions, the rate of uniform convergence is shown to be of order n ^-1. Moreover, a special case is considered where the c_jn are generated by a sequence of weight functions of a special structure.

Słowa kluczowe

EN

linear combinations; order statistics; Edgeworth expansions; rate of convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 277--302
• Opis fizyczny: Bibliogr.7 poz.

Twórcy

autor

Alberink B.

• Department of Mathematics University of Nijmegen, Postbus 9010 6500 GL, Nijmegen, The Netherlands

autor

Pap G.

• nstitute of Mathematics and Informatics, Lajos Kossuth University, P.O. Box 12 H-4010, Debrecen, Hungary

autor

van Zuijlen M. C. A.

• Department of Mathematics, University of Nijmegen, Postbus 9010 6500 GL, Nijmegen, The Netherlands

Bibliografia

• [1] V, Bentkiis, F. Götze and A. Tikhomirov, Berry-Esseen bound for statistics of weakly dependent samples, Bernoulli 3 (3997), pp. 329-350.
• [2] V. Bentkus, F, Götze and W. R. van Zwet, /In Edgeworth expansion for symmetric statistics, Ann, Statist. 25 (1997), pp. 851-896.
• [3] R. Helmers, Edgeworth expansions for linear combinations of order statistics, Math. Centre Tracts 105, Amsterdam 1982,
• [4] G. Pap and M. C, A. van Zuijlen, On the asymptotic behaviour of the Stringer bound, Statist. Neerlandica 50 (3) (1996), pp. 367-389.
• [5] G. Pap and M. C. A. van Zuijlen, A Berry-Esseen bound for linear combinations of order statistics, Statistics 31 (2) (1998), pp. 151-186.
• [6] W. R. Pestman, Mathematical Sfatistics, An Introduction, Walter de Gruyter, 1998.
• [7] W. R. van Zwet, A Berry-Esseen bound for symmetric statistics, Z. Wahrsch. verw. Gebiete 66 (1984), pp. 425 440.