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Multivariate Calculation

Use of the Continuous Groups

  • Book
  • © 1985

Overview

Authors:
  1. Roger H. Farrell

    1. Mathematics Department, Cornell University, Ithaca, USA

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction and Brief Survey

    • Roger H. Farrell
    Pages 1-12

  3. Transforms

    • Roger H. Farrell
    Pages 13-29

  4. Locally Compact Groups and Haar Measure

    • Roger H. Farrell
    Pages 30-50

  5. Wishart’s Paper

    • Roger H. Farrell
    Pages 51-63

  6. The Fubini-Type Theorems of Karlin

    • Roger H. Farrell
    Pages 64-86

  7. Manifolds and Exterior Differential Forms

    • Roger H. Farrell
    Pages 87-109

  8. Invariant Measures on Manifolds

    • Roger H. Farrell
    Pages 110-123

  9. Matrices, Operators, Null Sets

    • Roger H. Farrell
    Pages 124-162

  10. Examples Using Differential Forms

    • Roger H. Farrell
    Pages 163-177

  11. Cross-Sections and Maximal Invariants

    • Roger H. Farrell
    Pages 178-195

  12. Random Variable Techniques

    • Roger H. Farrell
    Pages 196-229

  13. The Construction of Zonal Polynomials

    • Roger H. Farrell
    Pages 230-297

  14. Problems for Users of Zonal Polynomials

    • Roger H. Farrell
    Pages 298-314

  15. Multivariate Inequalities

    • Roger H. Farrell
    Pages 315-357

  16. Back Matter

    Pages 358-376
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Keywords

About this book

Like some of my colleagues, in my earlier years I found the multivariate Jacobian calculations horrible and unbelievable. As I listened and read during the years 1956 to 1974 I continually saw alternatives to the Jacobian and variable change method of computing probability density functions. Further, it was made clear by the work of A. T. James that computation of the density functions of the sets of roots of determinental equations required a method other than Jacobian calculations and that the densities could be calculated using differential forms on manifolds. It had become clear from the work ofC S. Herz and A. T. James that the expression of the noncentral multivariate density functions required integration with respect to Haar measures on locally compact groups. Material on manifolds and locally compact groups had not yet reached the pages of multivariate books of the time and also much material about multivariate computations existed only in the journal literature or in unpublished sets oflecture notes. In spirit, being more a mathematician than a statistician, the urge to write a book giving an integrated treatment of these topics found expression in 1974-1975 when I took a one year medical leave of absence from Cornell University. During this period I wrote Techniques of Multivariate Calculation. Writing a coherent treatment of the various methods made obvious re­ quired background material.

Authors and Affiliations

  • Mathematics Department, Cornell University, Ithaca, USA

    Roger H. Farrell

Bibliographic Information

  • Book Title: Multivariate Calculation

  • Book Subtitle: Use of the Continuous Groups

  • Authors: Roger H. Farrell

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4613-8528-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1985

  • Softcover ISBN: 978-1-4613-8530-1Published: 21 October 2011

  • eBook ISBN: 978-1-4613-8528-8Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: 376

  • Topics: Applications of Mathematics

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