Accession Number : AD0248653

Title :   THE CANONICAL CORRELATION OF FUNCTIONS OF A RANDOM VECTOR

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : HANNAN, E.J.

Report Date : APR 1960

Pagination or Media Count : 1

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)

Descriptors :   COMPLEX VARIABLES, MEASURE THEORY, STATISTICAL PROCESSES.

Distribution Statement : APPROVED FOR PUBLIC RELEASE