LEADER 04815nam 22006374a 450 001 9910830436903321 005 20230617023841.0 010 $a1-280-27206-6 010 $a9786610272068 010 $a0-470-29876-6 010 $a0-470-86698-5 010 $a0-470-86699-3 035 $a(CKB)1000000000018899 035 $a(EBL)210562 035 $a(OCoLC)475919098 035 $a(SSID)ssj0000161433 035 $a(PQKBManifestationID)11151953 035 $a(PQKBTitleCode)TC0000161433 035 $a(PQKBWorkID)10198872 035 $a(PQKB)11543221 035 $a(MiAaPQ)EBC210562 035 $a(EXLCZ)991000000000018899 100 $a20040402d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeneralized least squares$b[electronic resource] /$fTakeaki Kariya, Hiroshi Kurata 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cWiley$dc2004 215 $a1 online resource (313 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-470-86697-7 320 $aIncludes bibliographical references (p. 281-286) and index. 327 $aContents; 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: CO[sub(2)] 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 327 $a3.3 A Nonlinear Version of the Gauss-Markov Theorem in Prediction3.4 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: CO[sub(2)] Emission Data; 4.7 Problems; 5 Serial Correlation Model; 5.1 Overview 327 $a5.2 Upper Bound for the Risk Matrix of a GLSE5.3 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 327 $a7.4 Nonlinear Versions of the Gauss-Markov Theorem7.5 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 327 $aA.1 Asymptotic Equivalence of the Estimators of ? in the AR(1) Error Model and Anderson ModelBibliography; Index; A; B; C; D; E; G; H; I; K; L; M; N; O; R; S; U; W 330 $aGeneralised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applicati 410 0$aWiley series in probability and statistics. 606 $aLeast squares 615 0$aLeast squares. 676 $a511 676 $a511.42 676 $a511/.42 700 $aKariya$b Takeaki$0102096 701 $aKurata$b Hiroshi$f1967-$0525079 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830436903321 996 $aGeneralized least squares$9822770 997 $aUNINA