On the variance of the number of maxima in random vectors and its applications

Annals of Applied Probability

Volumn 8, Issue 3, 1998, Pages 886-895

  Bai, Zhi Dong ^a   Chao, Chern Ching ^b   Hwang, Hsien Kuei ^b   Liang, Wen Qi ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Eulerian sums; Maximal points; Multicriterial optimization

Indexed keywords

EID: 0032222172     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903455     Document Type: Article

References (22)

1. BAILEY D. D., BORWEIN, J. M. and GIRGENSOHN, R. (1994). Experimental evaluation of Euler sums. Experiment. Math. 3 17-30.
2. BARNDORFF-NlELSEN, O. and SOBEL, M. (1966). On the distribution of the number of admissible points in a vector random sample. Theory Probab. Appl. 11 249-269.
3. BECKER, R. A., DENBY, L., MCGILL, R. and WILKS, A. R. (1987). Analysis of data from Places Rated Almanac. Amer. Statist. 41 169-186.
4. BENTLEY, J. L., CLARKSON, K. L. and LEVINE, D. B. (1993). Fast linear expected-time algorithms for computing maxima and convex hulls. Algorithmica 9 168-183.
5. BENTLEY, J. L., KUNG, H. T., SCHKOLNICK, M. and THOMPSON, C. D. (1978). On the average number of maxima in a set of vectors and applications. J. Assoc. Comput. Mach. 25 536-543.
6. BENTLEY, J. L. and SHAMOS, M. I. (1978). Divide and conquer for linear expected time. Inform. Process. Lett. 7 87-91.
7. BEREZOVSKII, B. A. and TRAVKIN, S. I. (1975). Supervision of queues of requests in computer systems. Automat. Remote Control 36 1719-1725.
8. BUCHTA, C. (1989). On the average number of maxima in a set of vectors. Inform. Process. Lett. 33 63-65.
9. DEVROYE, L. (1980). A note on finding convex hulls via maximal vectors. Inform. Process. Lett. 11 53-56.
10. DEVROYE, L. (1983). Moment inequalities for random variables in computational geometry. Computing 30 111-119.
11. DEVROYE, L. (1997). A note on the expected time for finding maxima by list algorithms. Algorithmica. To appear.
12. FLAJOLET, P. and GOLIN, M. (1993). Exact asymptotics of divide-and-conquer recurrences. Lecture Notes in Comput. Sci. 700 137-149. Springer, Berlin.
13. FLAJOLET, P. and SALVY, B. (1996). Euler sums and contour integral representations. Experiment. Math. To appear.
14. GOLIN, M. J. (1993). How many maxima can there be? Comput. Geom. 2 335-353.
15. HOFFMAN, M. E. (1992). Multiple harmonic sums. Pacific J. Math. 152 275-290.
16. IVANIN, V. M. (1975a). Asymptotic estimate for the mathematical expectation of the number of elements in the Pareto set. Cybernetics 11 108-113.
17. IVANIN, V. M. (1975b). Estimate of the mathematical expectation of the number of elements in a Pareto set. Cybernetics 11 506-507.
18. IVANIN, V. M. (1976). Calculation of the dispersion of the number of elements of the Pareto set for the choice of independent vectors with independent components. In Theory of Optimal Decisions 90-100. Akad. Nauk. Ukrain. SSR Inst. Kibernet., Kiev. (In Russian.)
19. O'NEILL, B. (1980). The number of outcomes in the Pareto-optimal set of discrete bargaining games. Math. Oper. Res. 6 571-578.
20. PREPARATA, F. P. and SHAMOS, M. I. (1985). Computational Geometry: An Introduction. Springer, New York.
21. SHOLOMOV, L. A. (1983). Survey of estimational results in choice problems. Engrg. Cybernetics 21 51-75.
22. ZAGIER, D. (1992). Values of zeta functions and their applications. In First European Congress of Mathematics 2 497-512. Birkhäuser, Berlin.