# The Coordinate-Free Approach to Gauss-Markov Estimation

Book

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

1. Front Matter
Pages I-VIII
2. Hilmar Drygas
Pages 1-7
3. Hilmar Drygas
Pages 8-45
4. Hilmar Drygas
Pages 46-109
5. Back Matter
Pages 110-117

### 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

1. 1.Studiengruppe für SystemforschungHeidelbergGermany

### Bibliographic information

• Book Title The Coordinate-Free Approach to Gauss-Markov Estimation
• Authors H. Drygas
• Series Title Lecture Notes in Operations Research and Mathematical Systems
• 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
• Softcover ISBN 978-3-540-05326-2
• eBook ISBN 978-3-642-65148-9
• Series ISSN 0075-8442
• Edition Number 1
• Number of Pages VIII, 118
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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