A Statistical Approach to Zonal Polynominals

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1983
Accession Number
ADA127624

Entities

People

  • Akimichi Takemura

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Data Science
  • Information Science
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics
  • Multivariate Analysis
  • Polynomials
  • Standards
  • Statistical Algorithms
  • Theses
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Instructional Design and Training Evaluation.
  • Linear Algebra

Technology Areas

  • Space