Monotone Dependence.

Abstract

Random variables X and Y are mutually completely dependent if there exists a one-to-one function g for which P(Y=g(X)) = 1. An example is presented of a pair of random variables which are mutually completely dependent, but 'almost' independent. This example motivates considering a new concept of dependence, called monotone dependence, in which g above is now required to be monotone. Finally, this monotone dependence concept leads to defining and studying the properties of a new numerical measure of statistical association between random variables X and Y defined by sup (corr (f(X), g(Y)), where the sup is taken over all pairs of suitable monotone functions f and g. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA037759

Entities

People

  • Allan R. Sampson
  • George Kimeldorf

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Demography
  • Integral Transforms
  • Mathematical Analysis
  • Monotone Functions
  • New York
  • Probability
  • Random Variables
  • Scientific Research
  • Sequences
  • Statistical Inference
  • Statistics
  • Translations
  • United States
  • United States Government
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Analytical Mechanics
  • Materials Science and Engineering.