Linear models: an integrated approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, N.J.
World Scientific
c2003
|
| Schriftenreihe: | Series on multivariate analysis
v. 6 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 587-606) and index 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 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 |
| Beschreibung: | 1 Online-Ressource (xxi, 622 p.) |
| ISBN: | 9789812564900 9810245920 981256490X |
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| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804175584948912128 |
|---|---|
| any_adam_object | |
| author | Sengupta, Debasis |
| author_facet | Sengupta, Debasis |
| author_role | aut |
| author_sort | Sengupta, Debasis |
| author_variant | d s ds |
| building | Verbundindex |
| bvnumber | BV043138411 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)228136576 (DE-599)BVBBV043138411 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:37Z |
| institution | BVB |
| isbn | 9789812564900 9810245920 981256490X |
| language | English |
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| series2 | Series on multivariate analysis |
| spelling | Sengupta, Debasis Verfasser aut Linear models an integrated approach Debasis Sengupta, Sreenivasa Rao Jammalamadaka River Edge, N.J. World Scientific c2003 1 Online-Ressource (xxi, 622 p.) txt rdacontent c rdamedia cr rdacarrier Series on multivariate analysis v. 6 Includes bibliographical references (p. 587-606) and index 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 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 MATHEMATICS / Probability & Statistics / General bisacsh Analysis of covariance fast Linear models (Statistics) fast Regression analysis fast Linear models (Statistics) Analysis of covariance Regression analysis Lineares Modell (DE-588)4134827-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Lineares Modell (DE-588)4134827-8 s 1\p DE-604 Jammalamadaka, S. Rao Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=135173 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sengupta, Debasis Linear models an integrated approach MATHEMATICS / Probability & Statistics / General bisacsh Analysis of covariance fast Linear models (Statistics) fast Regression analysis fast Linear models (Statistics) Analysis of covariance Regression analysis Lineares Modell (DE-588)4134827-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4056995-0 |
| title | Linear models an integrated approach |
| title_auth | Linear models an integrated approach |
| title_exact_search | Linear models an integrated approach |
| title_full | Linear models an integrated approach Debasis Sengupta, Sreenivasa Rao Jammalamadaka |
| title_fullStr | Linear models an integrated approach Debasis Sengupta, Sreenivasa Rao Jammalamadaka |
| title_full_unstemmed | Linear models an integrated approach Debasis Sengupta, Sreenivasa Rao Jammalamadaka |
| title_short | Linear models |
| title_sort | linear models an integrated approach |
| title_sub | an integrated approach |
| topic | MATHEMATICS / Probability & Statistics / General bisacsh Analysis of covariance fast Linear models (Statistics) fast Regression analysis fast Linear models (Statistics) Analysis of covariance Regression analysis Lineares Modell (DE-588)4134827-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Analysis of covariance Linear models (Statistics) Regression analysis Lineares Modell Statistik |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=135173 |
| work_keys_str_mv | AT senguptadebasis linearmodelsanintegratedapproach AT jammalamadakasrao linearmodelsanintegratedapproach |