By H. Drygas
These notes originate from a number of lectures which have been given within the Econometric Workshop of the heart for Operations examine and Econometrics (CORE) on the Catholic collage of Louvain. The members of the seminars have been urged to learn the 1st 4 chapters of Seber's ebook , however the exposition of the fabric went past Seber's exposition, if it appeared beneficial. Coordinate-free tools aren't new in Gauss-Markov estimation, in addition to Seber the paintings of Kolmogorov , SCheffe , Kruskal ,  and Malinvaud ,  could be pointed out. Malinvaud's strategy even though is a bit diverse from that of the opposite authors, simply because his optimality criterion relies at the ellipsoid of c- centration. This criterion is although corresponding to the standard c- cept of minimum covariance-matrix and for that reason the outcome needs to be an identical in either circumstances. whereas the standard conception offers no indication how small the covariance-matrix might be made earlier than the optimum es timator is computed, Malinvaud can exhibit how small the ellipsoid of focus might be made: it really is at such a lot equivalent to the intersection of the ellipssoid of focus of the saw random vector and the linear area during which the (unknown) expectation worth of the saw random vector is mendacity. This exposition is predicated at the commentary, that during regression ~nalysis and similar fields conclusions are or should still otherwise be utilized repeatedly.