The Coordinate-Free Approach to Gauss-Markov Estimation

  • Hilmar Drygas

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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Hilmar Drygas
    Pages 8-45
  3. Hilmar Drygas
    Pages 46-109
  4. Back Matter
    Pages 110-117

About this book

Introduction

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.

Keywords

Markov econometrics operations research regression statistical models

Authors and affiliations

  • Hilmar Drygas
    • 1
  1. 1.Studiengruppe für SystemforschungHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65148-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1970
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-05326-2
  • Online ISBN 978-3-642-65148-9
  • Series Print ISSN 0075-8442
  • About this book