# Accession Number:

## AD0248653

# Title:

## THE CANONICAL CORRELATION OF FUNCTIONS OF A RANDOM VECTOR

# Descriptive Note:

# Corporate Author:

## NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1960-04-01

# Pagination or Media Count:

## 1.0

# 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. Lancasters 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