Generalized least squares /
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| Author / Creator: | Kariya, Takeaki. |
|---|---|
| Imprint: | Chichester, West Sussex ; Hoboken, NJ : Wiley, c2004. |
| Description: | xiii, 289 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Wiley series in probability and statistics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5338443 |
Table of Contents:
- 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 GaussûMarkov Theorem.
- 3.1. Overview
- 3.2. Generalized Least Squares Predictors
- 3.3. A Nonlinear Version of the GaussûMarkov Theorem in Prediction
- 3.4. A Nonlinear Version of the GaussûMarkov 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 GaussûMarkov Theorem.
- 7.1. Overview
- 7.2. An Equivalence Relation on S(n
- 7.3. A Maximal Extension of the GaussûMarkov Theorem
- 7.4. Nonlinear Versions of the GaussûMarkov Theorem
- 7.5. Problems
- 8. Some Further Extensions.
- 8.1. Overview
- 8.2. Concentration Inequalities for the GaussûMarkov 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 GaussûMarkov 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
