Bounds on expectation of order statistics from a finite population

Journal of Statistical Planning and Inference

Volumn 113, Issue 2, 2003, Pages 569-588

  Balakrishnan, N ^a   Charalambides, C ^b   Papadatos, N ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

Expectation bounds; Finite population; Order statistics; Without replacement scheme

Indexed keywords

EID: 0037408773     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(01)00321-4     Document Type: Article

References (32)

1. Arnold, B.C., 1985. p-Norm bounds on the expectation of the maximum of possibly dependent sample. J. Multivariate Anal. 17, 316-332.
2. Arnold, B.C., Balakrishnan, N., 1989. Relations, bounds and approximations for order statistics. Lecture Notes in Statistics, Vol. 53. Springer, New York.
3. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N., 1992. A First Course in Order Statistics. Wiley, New York.
4. Arnold, B.C., Groeneveld, R.A., 1979. Bounds on expectations of linear systematic statistics based on dependent samples. Ann. Statist. 7, 220-223 (Correction 8, 1401).
5. Balakrishnan, A.V., 1981. Applied Functional Analysis, 2nd Edition. Springer, New York.
6. Balakrishnan, N., 1993. A simple application of the binomial-negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants. Statist. Probab. Lett. 18, 301-305.
7. Balakrishnan, N., Balasubramanian, K., 1993. Equivalence of Hartley-David-Gumbel and Papathanasiou bounds and some further remarks. Statist. Probab. Lett. 16, 39-41.
8. Billingsley, P., 1986. Probability and Measure, 2nd Edition. Wiley, New York.
9. Boland, P.J., Hollander, M., Joag-Dev, K., Kochar, S., 1996. Bivariate dependence properties of order statistics. J. Multivariate Anal. 56, 75-89.
10. Boyd, A.V., 1971. Bounds on order statistics. Publications of the Electrotechnical Faculty of Belgrade University, Mathematics and Physics Series, Vol. 365, pp. 31-32.
11. David, H.A., 1981. Order Statistics, 2nd Edition. Wiley, New York.
12. Fahmy, S., Proschan, F., 1981. Bounds on differences of order statistics. Amer. Statist. 35, 46-47.
13. Gumbel, E.J., 1954. The maxima of the mean largest value and of the range. Ann. Math. Statist. 25, 76-84.
14. Hájek, J., 1981. Sampling from a Finite Population. Marcel Dekker, New York.
15. Hartley, H.O., David, H.A., 1954. Universal bounds for mean range and extreme observations. Ann. Math. Statist. 25, 85-99.
16. Hawkins, D.M., 1971. On the bounds of the range of order statistics. J. Amer. Statist. Assoc. 66, 644-645.
17. Kochar, S.C., Korwar, R., 1997. Stochastic properties of order statistics from finite populations. Sankhyā Ser. A 59, 102-116.
18. Mallows, C.L., Richter, D., 1969. Inequalities of Chebychev type involving conditional expectations. Ann. Math. Statist. 40, 1922-1932.
19. Moriguti, S., 1951. Extremal properties of extreme value distributions. Ann. Math. Statist. 22, 523-536.
20. Moriguti, S., 1953. A modification of Schwarz's inequality with applications to distributions. Ann. Math. Statist. 24, 107-113.
21. Olkin, I., 1992. A matrix formulation on how deviant an observation can be. Amer. Statist. 46, 205-209.
22. Papadatos, N., 1997. Exact bounds for the expectations of order statistics from non-negative populations. Ann. Inst. Statist. Math. 49, 727-736.
23. Papadatos, N., 1999. Upper bound for the covariance of extreme order statistics from a sample of size three. Sankhyā Ser. A 61, 229-240.
24. Papathanasiou, V., 1990. Some characterizations of distributions based on order statistics. Statist. Probab. Lett. 9, 145-147.
25. Plackett, R.L., 1947. Limits of the ratio of mean range to standard deviation. Biometrika 34, 120-122.
26. Rychlik, T., 1993. Sharp bounds on L-estimates and their expectations for dependent samples. Commun. Statist. Theory Methods 22, 1053-1068 (Erratum 23, 305-306).
27. Rychlik, T., 1998. Bounds for expectations of L-estimates. In: Balakrishnan, N., Rao, C.R. (Eds.), Handbook of Statistics-16, Order Statistics: Theory and Methods. North-Holland, Amsterdam, pp. 105-145.
28. Scott, J.M.C., 1936. Appendix to paper by Pearson and Chandra Sekar. Biometrika 28, 319-320.
29. Takahasi, K., Futatsuya, M., 1998. Dependence between order statistics in samples from a finite population and its application to ranked set sampling. Ann. Inst. Statist. Math. 50, 49-70.
30. Terrell, G.R., 1983. A characterization of rectangular distributions. Ann. Probab. 11, 823-826.
31. Thomson, G.W., 1955. Bounds for the ratio of range to standard deviation. Biometrika 42, 268-269.
32. Wolkowicz, H., Styan, G.P.H., 1979. Extensions of Samuelson's inequality. Amer. Statist. 33, 143-144.