Subset complement addition upper bounds - an improved inclusion-exclusion method

Donald R. Hoover

doi:10.1016/0378-3758(90)90041-R

Subset complement addition upper bounds - an improved inclusion-exclusion method

Donald R. Hoover

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

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 Hunter's (1976) improved Bonferroni bounds. The SCAUB inequality is much simplier to calculate than are other distribution free upper bounds proposed in the past. It is also a distribution free analog of Glaz and Johnson's (1984) product type bounds. We prove that for any fixed n events, the SCAUB inequality monotonically decreases with k. SCAUB upper bounds are applied to the multivariate normal (or t) simultaneous inference interval problem.

Original language	English (US)
Pages (from-to)	195-202
Number of pages	8
Journal	Journal of Statistical Planning and Inference
Volume	24
Issue number	2
DOIs	https://doi.org/10.1016/0378-3758(90)90041-R
State	Published - Feb 1990
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

Bonferroni bound
Hunter bound
inclusion-exclusion
multivariate normal distributions
simultaneous inference

Access to Document

10.1016/0378-3758(90)90041-R

Cite this

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title = "Subset complement addition upper bounds - an improved inclusion-exclusion method",

abstract = "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 Hunter's (1976) improved Bonferroni bounds. The SCAUB inequality is much simplier to calculate than are other distribution free upper bounds proposed in the past. It is also a distribution free analog of Glaz and Johnson's (1984) product type bounds. We prove that for any fixed n events, the SCAUB inequality monotonically decreases with k. SCAUB upper bounds are applied to the multivariate normal (or t) simultaneous inference interval problem.",

keywords = "Bonferroni bound, Hunter bound, inclusion-exclusion, multivariate normal distributions, simultaneous inference",

author = "Hoover, \{Donald R.\}",

note = "Funding Information: * Partial support for this work was provided by The Office of Naval Research Contract Number NO0014 K 0156 while the author was a Ph.D. student. The author would like to thank Herbert Solomon, Ingram Olkin and several faculty members at the University of South Carolina for their helpful comments.",

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T1 - Subset complement addition upper bounds - an improved inclusion-exclusion method

AU - Hoover, Donald R.

N1 - Funding Information: * Partial support for this work was provided by The Office of Naval Research Contract Number NO0014 K 0156 while the author was a Ph.D. student. The author would like to thank Herbert Solomon, Ingram Olkin and several faculty members at the University of South Carolina for their helpful comments.

PY - 1990/2

Y1 - 1990/2

N2 - 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 Hunter's (1976) improved Bonferroni bounds. The SCAUB inequality is much simplier to calculate than are other distribution free upper bounds proposed in the past. It is also a distribution free analog of Glaz and Johnson's (1984) product type bounds. We prove that for any fixed n events, the SCAUB inequality monotonically decreases with k. SCAUB upper bounds are applied to the multivariate normal (or t) simultaneous inference interval problem.

AB - 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 Hunter's (1976) improved Bonferroni bounds. The SCAUB inequality is much simplier to calculate than are other distribution free upper bounds proposed in the past. It is also a distribution free analog of Glaz and Johnson's (1984) product type bounds. We prove that for any fixed n events, the SCAUB inequality monotonically decreases with k. SCAUB upper bounds are applied to the multivariate normal (or t) simultaneous inference interval problem.

KW - Bonferroni bound

KW - Hunter bound

KW - inclusion-exclusion

KW - multivariate normal distributions

KW - simultaneous inference

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UR - https://www.scopus.com/pages/publications/38249021132#tab=citedBy

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DO - 10.1016/0378-3758(90)90041-R

M3 - Article

AN - SCOPUS:38249021132

SN - 0378-3758

VL - 24

SP - 195

EP - 202

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 2

ER -

Subset complement addition upper bounds - an improved inclusion-exclusion method

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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