Deriving and Applying Improved Upper Bounds for Multivariate Normal Probability Outside of N-Cubes

Abstract

Two related improved Bonferroni methods to obtain upper bounds for the probabilities of unions of events are described. One procedure (bivariate method) uses probabilities of events and pairwise intersections of events. The other superior and more complicated procedure (trivariate method) uses probabilities of pairwise and three way intersections of events. These new methods are applied to multivariate normal hypothesis testing and simultaneous unbiased confidence intervals and are shown to give results superior to those of the currently used procedure (conservative assumption and independence of events) if the number of variables is not too large and the data is highly correlated. Modifications of these new methods to non-normal probabilities and different types of probability regions are also mentioned. Keywords: Statistical processes.

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Document Details

Document Type
Technical Report
Publication Date
Jul 19, 1988
Accession Number
ADA198193

Entities

People

  • Donald R. Hoover

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms
  • Biomedical

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computer Programs
  • Computers
  • Covariance
  • Data Science
  • Information Science
  • Integrals
  • Intervals
  • Normal Distribution
  • Order Statistics
  • Probability
  • Public Health
  • Random Variables
  • Statistics
  • Three Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.