Comparisons of Improved Bonferroni and Sidak/Slepian Bounds with Applications to Normal Markov Processes

Abstract

The recent literature contains theorems improving on both the Standard Bonferroni inequality and the Sidak/Slepian inequalities. The application of these improved theorems to upper bounds for non-coverage of simultaneous confidence intervals on multivariate normal variables is explored. The improved Bonferroni upper bounds will always apply, while improved Sidak/ Slepian bounds only apply to special cases. The improved Sidak/Slepian upper bound, if it applies, is always superior to the equivalent improved Bonferroni bound. This improvement, however, is not great when both methods are used to determine upper bounds for Type I error in the range of .01 to .10. It is shown that improved Sidak/Slepian bounds will apply to Normal Markov Processes, a commonly occurring and easily identifiable class of multivariate normal variables.

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Document Details

Document Type
Technical Report
Publication Date
Feb 23, 1989
Accession Number
ADA206699

Entities

People

  • Donald R. Hoover

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computational Science
  • Covariance
  • Inequalities
  • Intervals
  • Markov Chains
  • Markov Processes
  • Military Research
  • Multivariate Analysis
  • New York
  • Normal Distribution
  • Probability
  • Random Variables
  • South Carolina
  • Standards
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.