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The Coordinate-Free Approach to Gauss-Markov Estimation

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  • © 1970

Overview

Authors:
  1. Hilmar Drygas

    1. Studiengruppe für Systemforschung, Heidelberg, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 40)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Justification of the coordinate-free approach

    • Hilmar Drygas
    Pages 1-7

  3. Vector-spaces

    • Hilmar Drygas
    Pages 8-45

  4. Linear Statistical Models

    • Hilmar Drygas
    Pages 46-109

  5. Back Matter

    Pages 110-117
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Keywords

About this book

These notes originate from a couple of lectures which were given in the Econometric Workshop of the Center for Operations Research and Econometrics (CORE) at the Catholic University of Louvain. The participants of the seminars were recommended to read the first four chapters of Seber's book [40], but the exposition of the material went beyond Seber's exposition, if it seemed necessary. Coordinate-free methods are not new in Gauss-Markov estimation, besides Seber the work of Kolmogorov [11], SCheffe [36], Kruskal [21], [22] and Malinvaud [25], [26] should be mentioned. Malinvaud's approach however is a little different from that of the other authors, because his optimality criterion is based on the ellipsoid of c- centration. This criterion is however equivalent to the usual c- cept of minimal covariance-matrix and therefore the result must be the same in both cases. While the usual theory gives no indication how small the covariance-matrix can be made before the optimal es­ timator is computed, Malinvaud can show how small the ellipsoid of concentration can be made: it is at most equal to the intersection of the ellipssoid of concentration of the observed random vector and the linear space in which the (unknown) expectation value of the observed random vector is lying. This exposition is based on the observation, that in regression ~nalysis and related fields two conclusions are or should preferably be applied repeatedly.

Authors and Affiliations

  • Studiengruppe für Systemforschung, Heidelberg, Germany

    Hilmar Drygas

Bibliographic Information

  • Book Title: The Coordinate-Free Approach to Gauss-Markov Estimation

  • Authors: Hilmar Drygas

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-65148-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1970

  • Softcover ISBN: 978-3-540-05326-2Published: 01 January 1970

  • eBook ISBN: 978-3-642-65148-9Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: VIII, 118

  • Topics: Operations Research/Decision Theory

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