Bounds on the bias of approximation of fractional record values

• Autorzy: Bieniek M. , Bieniek M. , Szynal D.
• Języki publikacji: EN

Abstrakty

EN

We present sharp bounds for an approximation of fractional kth record values by convex combinations of ordinary kth record values. The bounds are ex-pressed in different scale units measured in pth central absolute moments of the under-lying distribution. The distributions which attain the bounds are also specified. The bounds are derived by the projection method.

Słowa kluczowe

EN

fractional record values; projection method; Moriguti’s inequality; variation diminishing property

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2005
• Tom: Vol. 25, Fasc. 2
• Strony: 197--210
• Opis fizyczny: Bibliogr. 13 poz., tab.

Twórcy

autor

Bieniek M.

• Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

autor

Bieniek M.

• Faculty of Economics, Statistics and Econometrics Department, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 5, 20-031 Lublin, Poland

autor

Szynal D.

• Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, Records, Wiley, New York 1998.
• [2] M. Bieniek and D. Szynal, On the fractional record values, Probab. Math. Statist. 24 (2004), pp. 27-46.
• [3] M. Bieniek and D. Szynal, On the bias of estimators based on fractional record ualues (submitted).
• [4] K. Danielak, Sharp upper bounds for expectations of differences of order statistics in various scale units, Comm. Statist. Theory Methods 33 (2004), pp. 787-803.
• [5] K. Danielak and M. Z. Raqab, Shwp bounds for expectations of kth record increments, Aust. N. Z. J. Stat. 46 (2004), pp. 665-674.
• [6] W. Dziubdziela and B. Kopociński, Limiting properties of the kth record values, Appl. Math. (Warsaw) 15 (1976), pp. 187-190.
• [7] L. Gajek and A. Okolewski, Projection bounds on expectations of record statistics from restricted families, J. Statist. Plann. Inference 110 (2003), pp. 97-108.
• [8] S. Karlin and W. J. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, Wiley, New York 1966.
• [9] S. Moriguti, A modification of Schwarz's inequality with applications to distributions, Ann. Math. Statistics 24 (1953), pp. 107-113.
• [10] M. Z. Raqab, Projection p-norm bounds on the moments of kth record increments, J. Statist. Plann. Inference 124 (2004), pp. 301-315.
• [11] M. Z. Raqab, Sharp bounds on the error in approximating the means of record statistics by inverse hazard functions, Comm. Statist. Theory Methods 33 (2004), pp. 1527-1539.
• [12] T. Rychlik, Projecting Statistical Functionals, Lecture Notes in Statist., Vol. 160, Springer, New York 2001.
• [13] I. J. Schoenberg, On variation diminishing approximation methods, in: On Numerical Approximation. Proceedings of the Symposium, Madison, 1958, R. E. Langer (Ed.), University of Wisconsin Press, Madison 1959, pp. 249-274.