UID:
almahu_9947367093602882
Format:
1 online resource (244 p.)
ISBN:
1-281-02826-6
,
9786611028268
,
0-08-051029-9
Series Statement:
Probability and mathematical statistics
Content:
Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed mode
Note:
Description based upon print version of record.
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Front Cover; Linear Models: A Mean Model Approach; Copyright Page; Contents; Preface; Chapter 1. Linear Algebra and Related Introductory Topics; 1.1 Elementary Matrix Concepts; 1.2 Kronecker Products; 1.3 Random Vectors; Chapter 2. Multivariate Normal Distribution; 2.1 Multivariate Normal Distribution Function; 2.2 Conditional Distributions of Multivariate Normal Random Vectors; 2.3 Distributions of Certain Quadratic Forms; Chapter 3. Distributions of Quadratic Forms; 3.1 Quadratic Forms of Normal Random Vectors; 3.2 Independence; 3.3 The t and F Distributions; 3.4 Bhat's Lemma
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Chapter 4. Complete, Balanced Factorial Experiments4.1 Models That Admit Restrictions (Finite Models); 4.2 Models That Do Not Admit Restrictions (Infinite Models); 4.3 Sum of Squares and Covariance Matrix Algorithms; 4.4 Expected Mean Squares; 4.5 Algorithm Applications; Chapter 5. Least-Squares Regression; 5.1 Ordinary Least-Squares Estimation; 5.2 Best Linear Unbiased Estimators; 5.3 ANOVA Table for the Ordinary Least-Squares Regression Function; 5.4 Weighted Least-Squares Regression; 5.5 Lack of Fit Test; 5.6 Partitioning the Sum of Squares Regression
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5.7 The Model Y = XB + E in Complete, Balanced FactorialsChapter 6. Maximum Likelihood Estimation and Related Topics; 6.1 Maximum Likelihood Estimators of B and a2; 6.2 Invariance Property, Sufficiency, and Completeness; 6.3 ANOVA Methods for Finding Maximum Likelihood Estimators; 6.4 The Likelihood Ratio Test for HB = h; 6.5 Confidence Bands on Linear Combinations of B; Chapter 7. Unbalanced Designs and Missing Data; 7.1 Replication Matrices; 7.2 Pattern Matrices and Missing Data; 7.3 Using Replication and Pattern Matrices Together; Chapter 8. Balanced Incomplete Block Designs
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8.1 General Balanced Incomplete Block Design8.2 Analysis of the General Case; 8.3 Matrix Derivations of Kempthorne's Interblock and Intrablock Treatment Difference Estimators; Chapter 9. Less Than Full Rank Models; 9.1 Model Assumptions and Examples; 9.2 The Mean Model Solution; 9.3 Mean Model Analysis When cov(E) = a2ln; 9.4 Estimable Functions; 9.5 Mean Model Analysis When cov(E) = a2V; Chapter 10. The General Mixed Model; 10.1 The Mixed Model Structure and Assumptions; 10.2 Random Portion Analysis: Type I Sum of Squares Method
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10.3 Random Portion Analysis: Restricted Maximum Likelihood Method10.4 Random Portion Analysis: A Numerical Example; 10.5 Fixed Portion Analysis; 10.6 Fixed Portion Analysis: A Numerical Example; Appendix 1 Computer Output for Chapter 5; Appendix 2 Computer Output for Chapter 7; A2.1 Computer Output for Section 7.2; A2.2 Computer Output for Section 7.3; Appendix 3 Computer Output for Chapter 8; Appendix 4 Computer Output for Chapter 9; Appendix 5 Computer Output for Chapter 10; A5.1 Computer Output for Section 10.2; A5.2 Computer Output for Section 10.4; A5.3 Computer Output for Section 10.6
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References and Related Literature
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English
Additional Edition:
ISBN 0-12-508465-X
Language:
English
