GENERALIZED LEAST SQUARES

By W. KULAN

CONTENTS PRELIMINARIES OVERVIEW MULTIVARIATE NORMAL AND WISHART DISTRIBUTIONS ELLIPTICALLY SYMMETRIC DISTRIBUTIONS GROUP INVARIANCE PROBLEMS GENERALIZED LEAST SQUARES ESTIMATORS GENERAL LINEAR REGRESSION MODEL FINITENESS OF MOMENTS AND TYPICAL GLSES EMPIRICAL EXAMPLE: CO2 EMISSION DATA EMPIRICAL EXAMPLE: BOND PRICE DATA NONLINEAR VERSIONS OF THE GAUSS–MARKOV THEOREM GENERALIZED LEAST SQUARES PREDICTORS A NONLINEAR VERSION OF THE GAUSS–MARKOV THEOREM IN PREDICTION A NONLINEAR VERSION OF THE GAUSS–MARKOV THEOREM IN ESTIMATION AN APPLICATION TO GLSES WITH ITERATED RESIDUALS SUR AND HETEROSCEDASTIC MODELS GLSES WITH A SIMPLE COVARIANCE STRUCTURE UPPER BOUND FOR THE COVARIANCE MATRIX OF A GLSE UPPER BOUND PROBLEM FOR THE UZE IN AN SUR MODEL UPPER BOUND PROBLEMS FOR A GLSE IN A HETEROSCEDASTIC MODEL SERIAL CORRELATION MODEL UPPER BOUND FOR THE RISK MATRIX OF A GLSE UPPER BOUND PROBLEM FOR A GLSE IN THE ANDERSON MODEL UPPER BOUND PROBLEM FOR A GLSE IN A TWO-EQUATION HETEROSCEDASTIC MODEL EMPIRICAL EXAMPLE: AUTOMOBILE DATA NORMAL APPROXIMATION UNIFORM BOUNDS FOR NORMAL APPROXIMATIONS TO THE PROBABILITY DENSITY FUNCTIONS UNIFORM BOUNDS FOR NORMAL APPROXIMATIONS TO THE CUMULATIVE DISTRIBUTION FUNCTIONS EXTENSION OF GAUSS–MARKOV THEOREM AN EQUIVALENCE RELATION ON S(N) A MAXIMAL EXTENSION OF THE GAUSS–MARKOV THEOREM SOME FURTHER EXTENSIONS CONCENTRATION INEQUALITIES FOR THE GAUSS–MARKOV ESTIMATOR EF?CIENCY OF GLSES UNDER ELLIPTICAL SYMMETRY DEGENERACY OF THE DISTRIBUTIONS OF GLSES GROWTH CURVE MODEL AND GLSES CONDITION FOR THE IDENTICAL EQUALITY BETWEEN THE GME AND THE OLSE GLSES AND NONLINEAR VERSION OF THE GAUSS–MARKOV THEOREM ANALYSIS BASED ON A CANONICAL FORM EF?CIENCY OF GLSES