Inequalities for Joint Distributions of Quadratic Forms.

Abstract

Chebychev inequalities are given for joint central and noncentral distributions of k quadratic forms; these are sharpened when k = 2 using the canonical correlations of Hotelling. Complementary inequalities are found as versions of Markov's inequality. Applications are noted in ballistics, in statistical quality control, in establishing consistency of Gauss-Markov estimates under dependence, and in constructing conservative joint confidence sets depending on the underlying distribution only through its low order moments. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1979
Accession Number
ADA083033

Entities

People

  • D. R. Jensen

Organizations

  • Virginia Tech

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Ballistics
  • Classification
  • Convex Sets
  • Dispersions
  • Distribution Functions
  • Gaussian Distributions
  • Industrial Production
  • Inequalities
  • Military Research
  • Monotone Functions
  • Numbers
  • Probability
  • Quality Control
  • Statistics
  • Theorems
  • Virginia

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Statistical inference.