Subset complement addition upper bounds. An improved inclusion-exclusion method. (English) Zbl 0708.62028

This paper presents the ‘Subset Complement Addition Upper Bound’ (SCAUB) procedure which produces upper bounds for probabilities of unions of n events given that probabilities of unions and/or intersections of subsets including up to k events are known. The SCAUB method is an extension of D. Hunter’s [J. Appl. Probab. 13, 597-603 (1976; Zbl 0349.60007)] improved Bonferroni bounds.


62F25 Parametric tolerance and confidence regions
62F99 Parametric inference


Zbl 0349.60007
Full Text: DOI


[1] Bauer, P.; Hackel, P., The application of Hunter’s inequality in simultaneous testing, Biometr. J., 27, 25-28, (1985)
[2] Bonferroni, C.E., Teori statistica classi e calcolo delle probabilita, Pubbl. R. ist. suges. sci. econ. comm. firenze, 8, 1-62, (1936)
[3] Boole, G., The laws of thought, XIX, (1854), Open Court Chicago
[4] Dunnett, C.W., A multiple comparison procedure for comparing several treatments with a control, J. amer. statist. assoc., 50, 1096-1121, (1955) · Zbl 0066.12603
[5] Glaz, J., A comparison of bonferroni-type and product type inequalities in the presence of dependence, Proceedings 1987 symposium on statistics and probability, (1988), Hidden Valley, PA (to be published by IMS).
[6] Glaz, J.; Johnson, B., Probability inequalities for multivariate distributions with dependence structure, J. amer. statist. assoc., 79, 436-440, (1984) · Zbl 0546.62024
[7] Hoover, D., Improved bonferroni and sidak/Slepian bounds: comparisons and applications, University of south carolina statistics technical report no. 134, (1988)
[8] Hoppe, F.M., Iterating bonferroni bounds, Statist. probab. lett., 3, 121-125, (1985) · Zbl 0585.60021
[9] Hunter, D., An upper bound for the probability of a union, J. appl. probab., 13, 597-603, (1976) · Zbl 0349.60007
[10] IMSL library users manual, Vol. 3, (1982), IMSL Houston, TX, Ch. M.
[11] Kounias, E.; Marin, J., Best linear bonferroni bounds, SIAM J. appl. math., 30, 307-323, (1976) · Zbl 0334.60001
[12] Kruskal, J.B., On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. amer. math. soc., 7, 48-50, (1956) · Zbl 0070.18404
[13] Schervish, M., Multivariate normal probabilities with error bound, Appl. statist, 33, 81-94, (1984) · Zbl 0547.65097
[14] Stoline, P., The Hunter method of simultaneous inference and its recommended use for applications having large known correlation structures, J. amer. statist. assoc., 78, 366-370, (1983) · Zbl 0534.62051
[15] Tomescu, I., Hypertrees and bonferroni inequalities, J. combinat. theory ser. B, 41, 209-217, (1986) · Zbl 0595.05055
[16] Tydeman, J.; Mitchell, R., A note on the kounias and marin method of best linear bonferroni bounds, SIAM J. appl. math., 39, 177, (1980) · Zbl 0463.60014
[17] Worsley, K.J., Bonferroni (improved) wins again, Amer. statist., 39, 235, (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.