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Multivariate Calculation

Use of the Continuous Groups

  • Roger H. Farrell

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Roger H. Farrell
    Pages 1-12
  3. Roger H. Farrell
    Pages 13-29
  4. Roger H. Farrell
    Pages 30-50
  5. Roger H. Farrell
    Pages 51-63
  6. Roger H. Farrell
    Pages 64-86
  7. Roger H. Farrell
    Pages 87-109
  8. Roger H. Farrell
    Pages 110-123
  9. Roger H. Farrell
    Pages 124-162
  10. Roger H. Farrell
    Pages 163-177
  11. Roger H. Farrell
    Pages 178-195
  12. Roger H. Farrell
    Pages 196-229
  13. Roger H. Farrell
    Pages 230-297
  14. Roger H. Farrell
    Pages 298-314
  15. Roger H. Farrell
    Pages 315-357
  16. Back Matter
    Pages 358-376

About this book

Introduction

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books of the time and also much material about multivariate computations existed only in the journal literature or in unpublished sets oflecture notes.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.

Keywords

Covariance matrix Maxima Random variable Variance correlation

Authors and affiliations

  • Roger H. Farrell
    • 1
  1. 1.Mathematics DepartmentCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8528-8
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8530-1
  • Online ISBN 978-1-4613-8528-8
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site
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