Projection method for moment bounds on order statistics from restricted families I. Dependent case

Journal of Multivariate Analysis

Volumn 57, Issue 1, 1996, Pages 156-174

  Gajek, Lesław ^a   Rychlik, Tomasz ^a  

^a POLISH ACADEMY OF SCIENCES   (Poland)

Author keywords

Convex cone; Decreasing failure probability distribution; Decreasing failure rate distribution; Dependent identically distributed random variables; Exponential distribution; L estimate; Order statistic; Symmetric unimodal distribution; Uniform distribution

Indexed keywords

EID: 0030123865     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0027     Document Type: Article

References (16)

1. [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. [2] ARNOLD, B. C., AND BALAKRISHNAN, N. (1989). Relations, Bounds and Approximations for Order Statistics. Lecture Notes in Statistics, Vol. 53, Springer-Verlag, New York.
3. [3] BALAKRISHNAN, A. V. (1981). Applied Functional Analysis, 2nd ed., Springer-Verlag, New York.
4. [4] BARLOW, R. E., AND PROSCHAN, F. (1975). Statistical Analysis of Reliability and Life Testing. Holt, Rinehart, and Winston, New York.
5. [5] CARAUX, G., AND GASCUEL, O. (1992). Bounds on distribution functions of order statistics for dependent varieties. Statist. Probab. Lett. 14 103-105.
6. [6] CARAUX, G., AND GASCUEL, O. (1992). Bounds on expectations of order statistics via extremal dependences. Statist. Probab. Lett. 15 143-148.
7. [7] DAVID, H. A. (1981). Order Statistics, 2nd ed. Wiley, New York.
8. [8] DHARMADHIKARI, S., AND JOAG-DEV, K. (1988). Unimodality, Convexity, and Applications. Academic Press, Boston.
9. [9] LAI, T. L., AND ROBBINS, H. (1976). Maximally dependent random variables. Proc. Nat. Acad. Sci. U.S.A. 73 286-288.
10. [10] MALLOWS, C. L. (1969). Extrema of expectations of uniform order statistics. SIAM Rev. 11 410-411.
11. [11] PATEL, J. K. (1983). Hazard rate and other classifications of distributions. In Encyclopedia of Statistical Sciences (S. Kotz, N. L. Johnson and C. B. Read, Eds.), pp. 590-594. Wiley, New York.
12. [12] PROSCHAN, F. (1963). Theoretical explanations of observed decreasing failure rate. Technometrics 5 375-384.
13. [13] RYCHLIK, T. (1992). Stochastically extremal distributions of order statistics for dependent samples. Statist. Probab. Lett. 13 337-341.
14. [14] RYCHLIK, T. (1993). Bounds for expectation of L-estimates for dependent samples. Statistics 24 1-7.
15. [15] RYCHLIK, T. (1993). Bias-robustness of L-estimates of location against dependence. Statistics 24 9-15.
16. [16] RYCHLIK, T. (1993). Sharp bounds on L-estimates and their expectations for dependent samples. Commun. Statist. Theory Methods 22 1053-1068.