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Linear models :an integrated approach

  • 作者: Sengupta, Debasis.
  • 其他作者: Jammalamadaka, S. Rao.
  • 出版: River Edge, N.J. : World Scientific ©2003.
  • 稽核項: 1 online resource (xxi, 622 pages) :illustrations.
  • 叢書名: Series on multivariate analysis ;vol. 6
  • 標題: Analysis of covariance. , Probability & StatisticsGeneral. , Regression Analysis , Regression analysis. , Linear models (Statistics) , MATHEMATICS Probability & Statistics -- General. , Analyse de régression. , Electronic book. , Electronic books. , MATHEMATICS , Analyse de covariance.
  • ISBN: 9810245920 , 9789810245924
  • ISBN: 9810245920
  • 試查全文@TNUA:
  • 附註: Includes bibliographical references (pages 587-606) and index. Ch. 1. Introduction. 1.1. The linear model. 1.2. Why a linear model? 1.3. Description of the linear model and notations. 1.4. Scope of the linear model. 1.5. Related models. 1.6. Uses of the linear model. 1.7. A tour through the rest of the book. 1.8. Exercises -- ch. 2. Review of linear algebra. 2.1. Matrices and vectors. 2.2. Inverses and generalized inverses. 2.3. Vector space and projection. 2.4. Column space. 2.5. Matrix decompositions. 2.6. Löwner order. 2.7. Solution of linear equations. 2.8. Optimization of quadratic forms and functions. 2.9 Exercises -- ch. 3. Review of statistical results. 3.1. Covariance adjustment. 3.2. Basic distributions. 3.3. Distribution of quadratic forms. 3.4. Regression. 3.5. Basic concepts of inference. 3.6. Point estimation. 3.7. Bayesian estimation. 3.8. Tests of hypotheses. 3.9. Confidence region. 3.10. Exercises -- ch. 4. Estimation in the linear model. 4.1. Linear estimation: some basic facts. 4.2. Least squares estimation. 4.3. Best linear unbiased estimation. 4.4. Maximum likelihood estimation. 4.5. Fitted value, residual and leverage. 4.6. Dispersions. 4.7. Estimation of error variance and canonical decompositions. 4.8. Reparametrization. 4.9. Linear restrictions. 4.10. Nuisance parameters. 4.11. Information matrix and Cramer-Rao bound. 4.12. Collinearity in the linear model. 4.13. Exercises -- ch. 5. Further inference in the linear model. 5.1. Distribution of the estimators. 5.2. Confidence regions. 5.3. Tests of linear hypotheses. 5.4. Prediction in the linear model. 5.5. Consequences of collinearity. 5.6. Exercises -- ch. 6. Analysis of variance in basic designs. 6.1. Optimal design. 6.2. One-way classified data. 6.3. Two-way classified data. 6.4. Multiple treatment/block factors. 6.5. Nested models. 6.6. Analysis of covariance. 6.7. Exercises. Ch. 7. General linear model. 7.1. Why study the singular model? 7.2. Special considerations with singular models. 7.3. Best linear unbiased estimation. 7.4. Estimation of error variance. 7.5. Maximum likelihood estimation. 7.6. Weighted least squares estimation. 7.7. Some recipes for obtaining the BLUE. 7.8. Information matrix and Cramer-Rao bound. 7.9. Effect of linear restrictions. 7.10. Model with nuisance parameters. 7.11. Tests of hypotheses. 7.12. Confidence regions. 7.13. Prediction. 7.14. Exercises -- ch. 8. Misspecified or unknown dispersion. 8.1. Misspecified dispersion matrix. 8.2. Unknown dispersion: the general case. 8.3. Mixed effects and variance components. 8.4. Other special cases with correlated error. 8.5. Special cases with uncorrelated error. 8.6. Some problems of signal processing. 8.7. Exercises -- ch. 9. Updates in the general linear model. 9.1. Inclusion of observations. 9.2. Exclusion of observations. 9.3. Exclusion of explanatory variables. 9.4. Inclusion of explanatory variables. 9.5. Data exclusion and variable inclusion. 9.6. Exercises -- ch. 10. Multivariate linear model. 10.1. Description of the multivariate linear model. 10.2. Best linear unbiased estimation. 10.3. Unbiased estimation of error dispersion. 10.4. Maximum likelihood estimation. 10.5. Effect of linear restrictions. 10.6. Tests of linear hypotheses. 10.7. Linear prediction and confidence regions. 10.8. Applications. 10.9. Exercises -- ch. 11. Linear inference -- other perspectives. 11.1. Foundations of linear inference. 11.2. Admissible, Bayes and minimax linear estimators. 11.3. Biased estimators with smaller dispersion. 11.4. Other linear estimators. 11.5. A geometric view of BLUE in the linear model. 11.6. Large sample properties of estimators. 11.7. Exercises.
  • 摘要: Linear Models: An Integrated Approach aims to provide a clearand deep understanding of the general linear model using simplestatistical ideas. Elegant geometric arguments are also invoked asneeded and a review of vector spaces and matrices is provided to makethe treatment self-contained.
  • 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135173
  • 系統號: 005321641
  • 資料類型: 電子書
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Linear Models: An Integrated Approach aims to provide a clear and deep understanding of the general linear model using simple statistical ideas. Elegant geometric arguments are also invoked as needed and a review of vector spaces and matrices is provided to make the treatment self-contained. Complex, matrix-algebraic methods, such as those used in the rank-deficient case, are replaced by statistical proofs that are more transparent and that show the parallels with the simple linear model. This book has the following special features: Use of simple statistical ideas such as linear zero functions and covariance adjustment to explain the fundamental as well as advanced concepts Emphasis on the statistical interpretation of complex algebraic results A thorough treatment of the singular linear model, including the case of multivariate response A unified discussion on models with a partially unknown dispersion matrix, including mixed- effects/variance-components models and models for spatial,and time series data Insight into updates on the linear model and their connection with diagnostics, design, variable selection, the Kalman filter, etc. An extensive discussion on the foundations of linear inference, along with linear alternatives to least squares Coverage of other special topics, such as collinearity, stochastic and inequality constraints, misspecified models, etc. Simpler proofs of numerous known results Pointers to current research through examples and exercises
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