Generalized Least SquaresISBN: 978-0-470-86697-9
Hardcover
312 pages
July 2004
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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 θ in the AR(1) Error Model and Anderson Model.
Bibliography.
Index.
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