Accession Number:

ADA127624

Title:

A Statistical Approach to Zonal Polynominals

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA DEPT OF STATISTICS

Personal Author(s):

Report Date:

1983-01-01

Pagination or Media Count:

103.0

Abstract:

Zonal polynomials form one of the essential tools for expressing noncentral distributions arising in multivariate analysis. However, they have not been used very often or usually taught mainly because i the theory has been based on some branches of advanced mathematics, and ii the computational difficulty. In this dissertation a self-contained theory of zonal polynomials is developed in the framework of standard multivariate analysis. Zonal polynomials will be defined as characteristic vectors of a linear transformation in the vector space of homogeneous symmetric polynomials. From this definition almost all known properties of zonal polynomials are derived, as well as some new properties. In addition to theoretical considerations, computational aspects of zonal polynomials are discussed extensively.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE