Generalized Least Squares (eBook)

Takeaki Kariya, Hiroshi Kurata (Autoren)

eBook Download: PDF

2004 | 1. Auflage
312 Seiten
John Wiley & Sons (Verlag)
978-0-470-86698-6 (ISBN)

Infos

Generalised Least Squares adopts a concise and
mathematically rigorous approach. It will provide an
up-to-date self-contained introduction to the unified theory of
generalized least squares estimations, adopting a concise and
mathematically rigorous approach. The book covers in depth the
'lower and upper bounds approach', pioneered by the first author,
which is widely regarded as a very powerful and useful tool for
generalized least squares estimation, helping the reader develop
their understanding of the theory. The book also contains exercises
at the end of each chapter and applications to statistics,
econometrics, and biometrics, enabling use for self-study or as a
course text.

Autor

Takeaki Kariya is the author of Generalized Least Squares, published by Wiley. Hiroshi Kurata is the author of Generalized Least Squares, published by Wiley.

Inhalt

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 theta in
the AR(1) Error Model and Anderson Model.

Bibliography.

Index.

Rezensionen

"...provides a systematic discussion about statistical methods
and theory for handling linear regression analysis when such
conventional model assumptions are violated."
(Technometrics, November 2005)

"...an accessible introduction to GLSE...an excellent source of
reference, can be used as a course text, and will help to stimulate
further research into this flourishing topic..." (Mathematical
Reviews, 2005)

"...provides an up-to-date, self-contained introduction to the
unified theory ..." (Zentralblatt Math, Vol. 1057, No. 8.
2005)

Produkt-Details

• Erscheint lt. Verlag: 19.11.2004
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Angew. Wahrscheinlichkeitsrechn. u. Statistik / Modelle • Applied Probability & Statistics - Models • biometrics • Biometrie • Engineering statistics • Regression Analysis • Regressionsanalyse • Statistics • Statistik • Statistik in den Ingenieurwissenschaften • Technische Statistik
• ISBN-10: 0-470-86698-5 / 0470866985
• ISBN-13: 978-0-470-86698-6 / 9780470866986