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

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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 languageEnglish (US)
Pages (from-to)195-202
Number of pages8
JournalJournal of Statistical Planning and Inference
Volume24
Issue number2
DOIs
StatePublished - Feb 1990
Externally publishedYes

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

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