一般最小2乗法<br>Generalized Least Squares (Wiley Series in Probability and Statistics)

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一般最小2乗法
Generalized Least Squares (Wiley Series in Probability and Statistics)

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  • 製本 Hardcover:ハードカバー版/ページ数 289 p.
  • 言語 ENG
  • 商品コード 9780470866979
  • DDC分類 511.42

Full Description


"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.

Table of Contents

Preface                                            xi
Preliminaries 1 (24)
Overview 1 (1)
Multivariate Normal and Wishart 1 (7)
Distributions
Elliptically Symmetric Distributions 8 (8)
Group Invariance 16 (5)
Problems 21 (4)
Generalized Least Squares Estimators 25 (42)
Overview 25 (1)
General Linear Regression Model 26 (7)
Generalized Least Squares Estimators 33 (7)
Finiteness of Moments and Typical GLSEs 40 (9)
Empirical Example: CO2 Emission Data 49 (6)
Empirical Example: Bond Price Data 55 (8)
Problems 63 (4)
Nonlinear Versions of the Gauss--Markov 67 (30)
Theorem
Overview 67 (1)
Generalized Least Squares Predictors 68 (5)
A Nonlinear Version of the Gauss--Markov 73 (9)
Theorem in Prediction
A Nonlinear Version of the Gauss--Markov 82 (8)
Theorem in Estimation
An Application to GLSEs with Iterated 90 (5)
Residuals
Problems 95 (2)
SUR and Heteroscedastic Models 97 (46)
Overview 97 (5)
GLSEs with a Simple Covariance Structure 102(6)
Upper Bound for the Covariance Matrix of 108(9)
a GLSE
Upper Bound Problem for the UZE in an SUR 117(9)
Model
Upper Bound Problems for a GLSE in a 126(8)
Heteroscedastic Model
Empirical Example: CO2 Emission Data 134(6)
Problems 140(3)
Serial Correlation Model 143(28)
Overview 143(2)
Upper Bound for the Risk Matrix of a GLSE 145(8)
Upper Bound Problem for a GLSE in the 153(5)
Anderson Model
Upper Bound Problem for a GLSE in a 158(7)
Two-equation Heteroscedastic Model
Empirical Example: Automobile Data 165(5)
Problems 170(1)
Normal Approximation 171(24)
Overview 171(5)
Uniform Bounds for Normal Approximations 176(6)
to the Probability Density Functions
Uniform Bounds for Normal Approximations 182(11)
to the Cumulative Distribution Functions
Problems 193(2)
Extension of Gauss--Markov Theorem 195(18)
Overview 195(3)
An Equivalence Relation on S(n) 198(5)
A Maximal Extension of the Gauss--Markov 203(5)
Theorem
Nonlinear Versions of the Gauss--Markov 208(4)
Theorem
Problems 212(1)
Some Further Extensions 213(31)
Overview 213(1)
Concentration Inequalities for the 214(9)
Gauss--Markov Estimator
Efficiency of GLSEs under Elliptical 223(10)
Symmetry
Degeneracy of the Distributions of GLSEs 233(8)
Problems 241(3)
Growth Curve Model and GLSEs 244(30)
Overview 244(5)
Condition for the Identical Equality 249(1)
between the GME and the OLSE
GLSEs and Nonlinear Version of the 250(5)
Gauss-Markov Theorem
Analysis Based on a Canonical Form 255(7)
Efficiency of GLSEs 262(9)
Problems 271(3)
A Appendix 274(7)
A.1 Asymptotic Equivalence of the 274(7)
Estimators of θ in the AR(1) Error
Model and Anderson Model
Bibliography 281(6)
Index 287