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