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Mathematical statistics --- Linear models (Statistics) --- 519.235 --- Models, Linear (Statistics) --- Mathematical models --- Statistics --- Statistics of dependent variables. Contingency tables --- 519.235 Statistics of dependent variables. Contingency tables

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519.235 --- Regression analysis --- Analysis, Regression --- Linear regression --- Regression modeling --- 519.235 Statistics of dependent variables. Contingency tables --- Statistics of dependent variables. Contingency tables --- Multivariate analysis --- Structural equation modeling --- Mathematical statistics --- Regression analysis. --- Analyse de régression

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Mathematical statistics --- 519.235 --- Multivariate analysis --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- Statistics of dependent variables. Contingency tables --- Multivariate analysis. --- Methoden en technieken --- statistiek --- statistiek. --- 519.235 Statistics of dependent variables. Contingency tables --- Statistiek. --- Statistique mathematique --- Analyse multivariee

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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.

Mathematical statistics --- 519.235 --- Statistics of dependent variables. Contingency tables --- Business & Economics --- Economic Theory --- 519.235 Statistics of dependent variables. Contingency tables --- Estimation theory --- Regression Analysis --- Vector spaces --- Regression analysis --- Théorie de l'estimation --- Analyse de régression --- Espaces vectoriels --- Modèles linéaires (statistique) --- Linear models (Statistics) --- Modèles linéaires (statistique)

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Business economics --- Computer. Automation --- Mathematical statistics --- Economics --- Regression Analysis --- Analysis of variance --- 519.235 --- Regression analysis --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- ANOVA (Analysis of variance) --- Variance analysis --- Experimental design --- Statistics of dependent variables. Contingency tables --- 519.235 Statistics of dependent variables. Contingency tables