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{2}-Inverses and Their Statistical Application

  • Book
  • © 1988

Overview

Authors:
  1. Albert J. Getson

    1. Merck, Sharp and Dohme Research Laboratories, West Point, USA

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  2. Francis C. Hsuan

    1. Department of Statistics, School of Business Administration, Temple University, Philadelphia, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Statistics (LNS, volume 47)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Albert J. Getson, Francis C. Hsuan
    Pages 1-4

  3. Time For {2}-Inverses

    • Albert J. Getson, Francis C. Hsuan
    Pages 5-34

  4. {2}-Inverses, Quadratic forms and Second Degree Polynomials

    • Albert J. Getson, Francis C. Hsuan
    Pages 35-60

  5. {2}-Inverses and Least Square Solutions

    • Albert J. Getson, Francis C. Hsuan
    Pages 61-83

  6. {2}-Inverses in Linear Models

    • Albert J. Getson, Francis C. Hsuan
    Pages 84-106

  7. Back Matter

    Pages 107-111
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Keywords

About this book

Much of the traditional approach to linear model analysis is bound up in complex matrix expressions revolving about the usual generalized inverse. Motivated by this important role of the generalized inverse. the research summarized here began as an interest in understanding. in geometric terms. the four conditions defining the qnique Moore-Penrose Inverse. Such an investigation. it was hoped. might lead to a better understanding. and possibly a simplification of. the usual matrix expressions. Initially this research was begun by Francis Hsuan and Pat Langenberg, without knowledge of Kruskal's paper published in 1975. This oversight was perhaps fortu­ nate. since if they had read his paper they may not have continued their effort. A summary of this early research appears in Hsuan. Langenberg and Getson (1985). This monograph is a summary of the research on {2}-inverses continued by Al Getson. while a graduate student. in collaboration with Francis Hsuan of the Depart­ ment of Statistics. School of Business Administration. at Temple University. Philadelphia. The literature on generalized inverses and related topics is extensive and some of what is present here has appeared elsewhere. Generally. this literature is not presented from the point of view of {2}-inverses. We have tried to do justice to . the relevant published works and appologize for those we have either overlooked or possibly misrepresented.

Authors and Affiliations

  • Merck, Sharp and Dohme Research Laboratories, West Point, USA

    Albert J. Getson

  • Department of Statistics, School of Business Administration, Temple University, Philadelphia, USA

    Francis C. Hsuan

Bibliographic Information

  • Book Title: {2}-Inverses and Their Statistical Application

  • Authors: Albert J. Getson, Francis C. Hsuan

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-3930-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-0-387-96849-0Published: 28 November 1988

  • eBook ISBN: 978-1-4612-3930-7Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 110

  • Topics: Algebra

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