THE CANONICAL CORRELATION OF FUNCTIONS OF A RANDOM VECTOR

Abstract

The classical theory of canonical correlation is concerned with a standard description of the relationship between any linear combination of p random variables x and any linear combination of q random variables y insofar as this relation can be described in terms of correlation. Lancaster extended this theory to include a description of the correlation of any functions of x and y (which have finite variances) for a (over) class of joint distributions of x and y which is very general. Lancaster's results are now derived in a fashion which lends itself easily to generalizations to the case where p and q are not finite. In the case of Gaussian, stationary, processes this generalization is equivalent to the classical spectral theory and corresponds to a canonical reduction of a (finite) sample of data which is basic. The theory also then extends to any number of processes. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1960
Accession Number
AD0248653

Entities

People

  • E.j. Hannan

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Random Variables
  • Standards
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis