Bounds for expectation of l-estimates for dependent samples

Statistics

Volumn 24, Issue 1, 1993, Pages 1-7

  Rychlik, Tomasz ^a  

^a INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

bounds on expectation; Dependent sample; extreme point; identically distributed sample; L estimate; order statistic; stochastic ordering

Indexed keywords

EID: 0002509284     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331888308802385     Document Type: Article

References (20)

1. Arnold, B. C. (1980). Distribution-free bounds on the mean of the maximum of a dependent sample. SIAM J. Appl. Math. 38, 163–167.
2. Arnold. B. C. (1985). p-Norm bounds on the expectation of the maximum of possibly dependent sample. J. Multivar. Anal. 17, 316–332.
3. Arnold, B. C. and Balakrishnan, N. (1989). Relations, Bounds and Approximations for Order Statistics. Lecture Notes in Statist. 53, Springer, New York.
4. Arnold, B. C. and Groeneveld, R. A. (1974). Bounds for deviations between sample population statistics. Biometriko 61, 387–389.
5. Arnold, B. C. and Groeneveld, R. A. (1979). Bounds on expectations of linear systematic statistics based on dependent samples. Ann. Statist. 7, 220–223.
6. David, H. A. (1986). Inequalities for ordered sums. Ann. Inst. Statist. Math. 38, 551–555.
7. David, H. A. (1988). General bounds and inequalities in order statistics. Commun. Statist.-Theor. Meth. 17, 2119–2133.
8. Fahmy, S. and Proschan, F. (1981). Bounds on differences of order statistics. Amer. Statist. 35, 46-47.
9. Gilstein, C. Z. (1981). Bounds for expectations of linear combinations of order statistics (preliminary report). Inst. Math. Statist. Bull. 10, 253.
10. Groeneveld, R. A. (1982). Best bounds for order statistics and their expectations in range and mean units with applications. Commun. Statist.-Theor. Meth. 11, 1809–1815.
11. Hoover, D. R. (1989). Bounds on expectations of order statistics for dependent samples. Statist. Prob. Letters 8, 261–265.
12. Lai, T. L. and Robbins, H. (1976). Maximally dependent random variables. Proc. Nat. Acad. Sci. U.S.A. 73, 286–288.
13. Mallows, C. L. (1969). Extrema of expectations of uniform order statistics. SIAM Rev. 11, 410–411.
14. Mallows, C. L. and Richter, D. (1969). Inequalities of Chebyshev type involving conditional expectations. Ann. Math. Statist. 40, 1922–1932.
15. Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and its Applications. Academic Press, New York.
16. Rockafellar, R. T. (1970). Convex Analysis. Princeton Univ. Press, Princeton
17. Rychlik, T. (1992). Stochastically extremal distributions of order statistics for dependent samples. Statist. Prob. Letters 13, 337–341.
18. Samuelson, P.A. (1968). How deviant can you be? J. Amer. Statist. Assoc. 63, 1522–1525.
19. Smith, N. L. and Tong, Y. L. (1983). Inequalities for functions of order statistics under an additive model. Ann. Inst. Statist. Math. 35, 255–265.
20. Wolkowicz, H. and Styan, G. P. H. (1979). Extensions of Samuelson's inequality. Amer. Statist. 33, 143–144.