Generalized Least Squares

Preface. 1 Preliminaries. 1.1 Overview. 1.2 Multivariate Normal and Wishart Distributions. 1.3 Elliptically Symmetric Distributions. 1.4 Group Invariance. 1.5 Problems. 2 Generalized Least Squares Estimators. 2.1 Overview. 2.2 General Linear Regression Model. 2.3 Generalized Least Squares Estimators. 2.4 Finiteness of Moments and Typical GLSEs. 2.5 Empirical Example: CO2 Emission Data. 2.6 Empirical Example: Bond Price Data. 2.7 Problems. 3 Nonlinear Versions of the Gauss-Markov Theorem. 3.1 Overview. 3.2 Generalized Least Squares Predictors. 3.3 A Nonlinear Version of the Gauss-Markov Theorem in Prediction. 3.4 A Nonlinear Version of the Gauss-Markov Theorem in Estimation. 3.5 An Application to GLSEs with Iterated Residuals. 3.6 Problems. 4 SUR and Heteroscedastic Models. 4.1 Overview. 4.2 GLSEs with a Simple Covariance Structure. 4.3 Upper Bound for the Covariance Matrix of a GLSE. 4.4 Upper Bound Problem for the UZE in an SUR Model. 4.5 Upper Bound Problems for a GLSE in a Heteroscedastic Model. 4.6 Empirical Example: CO2 Emission Data. 4.7 Problems. 5 Serial Correlation Model. 5.1 Overview. 5.2 Upper Bound for the Risk Matrix of a GLSE. 5.3 Upper Bound Problem for a GLSE in the Anderson Model. 5.4 Upper Bound Problem for a GLSE in a Two-equation Heteroscedastic Model. 5.5 Empirical Example: Automobile Data. 5.6 Problems. 6 Normal Approximation. 6.1 Overview. 6.2 Uniform Bounds for Normal Approximations to the Probability Density Functions. 6.3 Uniform Bounds for Normal Approximations to the Cumulative Distribution Functions. 6.4 Problems. 7 Extension of Gauss-Markov Theorem. 7.1 Overview. 7.2 An Equivalence Relation on S(n). 7.3 A Maximal Extension of the Gauss-Markov Theorem. 7.4 Nonlinear Versions of the Gauss-Markov Theorem. 7.5 Problems. 8 Some Further Extensions. 8.1 Overview. 8.2 Concentration Inequalities for the Gauss-Markov Estimator. 8.3 Efficiency of GLSEs under Elliptical Symmetry. 8.4 Degeneracy of the Distributions of GLSEs. 8.5 Problems. 9 Growth Curve Model and GLSEs. 9.1 Overview. 9.2 Condition for the Identical Equality between the GME and the OLSE. 9.3 GLSEs and Nonlinear Version of the Gauss-Markov Theorem . 9.4 Analysis Based on a Canonical Form. 9.5 Efficiency of GLSEs. 9.6 Problems. A. Appendix. A.1 Asymptotic Equivalence of the Estimators of ¸ in the AR(1) Error Model and Anderson Model. Bibliography. Index.