Linear models :: a mean model approach /
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 vect...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego :
Academic Press,
©1996.
|
| Schriftenreihe: | Probability and mathematical statistics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | 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 models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory. Key Features * Provides a versatile format for investigating linear model theory, using the mean model * Uses examples that are familiar to the student: * design of experiments, analysis of variance, regression, and normal distribution theory * Includes a review of relevant linear algebra concepts * Contains fully worked examples which follow the theorem/proof presentation. |
| Beschreibung: | 1 online resource (xii, 228 pages) |
| Bibliographie: | Includes bibliographical references (pages 221-223) and index. |
| ISBN: | 058549214X 9780585492148 9780125084659 012508465X 0080510299 9780080510293 |
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| 300 | |a 1 online resource (xii, 228 pages) | ||
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| 505 | 0 | |a Linear Algebra and Related Introductory Topics: Elementary Matrix Concepts. Kronecker Products. Random Vectors. Multivariate Normal Distribution: Multivariate Normal Distribution Function. Conditional Distributionsof Multivariate Normal Vectors. Distributions of Certain Quadratic Forms. Distributions of Quadratic Forms: Quadratic Forms of Normal Random Vectors. Independence. t and F Distributions. Bhats Lemma. Complete, Balanced Factorial Experiments: Models That Admit Restrictions (Finite Models). Models That Do Not Admit Restrictions (Infinite Models). Sum of Squares and Covariance Matrix Algorithms. Expected Mean Squares. Algorithm Applications. Least Squares Regression: Ordinary Least SquaresEstimation. Best Linear Unbiased Estimators. ANOVA Table for the Ordinary Least Squares Regression Function. Weighted Least Squares Regression. Lack of Fit Test. Partitioning the Sum of Squares Regression. The Model Y = X(+ E in Complete, BalancedFactorials. Maximum Likelihood Estimation and Related Topics: Maximum Likelihood Estimators (MLEs) of (and (<+>2. Invariance Property, Sufficiency and Completeness. ANOVA Methods for Finding Maximum Likelihood Estimators. The Likelihood Ratio Test for H(= h. Confidence Bands on Linear Combinations of (. Unbalanced Designs and Missing Data: Replication Matrices. Pattern Matrices and Missing Data. Using Replication and Pattern Matrices Together. Balanced Incomplete Block Designs: General Balanced Incomplete Block Design. Analysis of the General Case. Matrix Derivations of Kempthornes Inter- and Intra-Block Treatment Difference Estimators. Less Than Full Rank Models: Model Assumptions and Examples. The Mean Model Solution. Mean Model Analysis When cov(E) = (<+>2I<->n. Estimable Functions. Mean Model Analysis When cov(E) = (<+>2V. The General Mixed Model: The Mixed Model Structure and Assumptions. Random Portion Analysis: Type I Sumof Squares Method. Random Portion Analysis: Restricted Maximum Likelihood Method. Random Portion Analysis: A Numerical Example. Fixed Portion Analysis. Fixed Portion Analysis: A Numerical Example. Appendixes. References. Subject Index. | |
| 520 | |a 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 models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory. Key Features * Provides a versatile format for investigating linear model theory, using the mean model * Uses examples that are familiar to the student: * design of experiments, analysis of variance, regression, and normal distribution theory * Includes a review of relevant linear algebra concepts * Contains fully worked examples which follow the theorem/proof presentation. | ||
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| 653 | 0 | |a Statistical analysis | |
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| contents | Linear Algebra and Related Introductory Topics: Elementary Matrix Concepts. Kronecker Products. Random Vectors. Multivariate Normal Distribution: Multivariate Normal Distribution Function. Conditional Distributionsof Multivariate Normal Vectors. Distributions of Certain Quadratic Forms. Distributions of Quadratic Forms: Quadratic Forms of Normal Random Vectors. Independence. t and F Distributions. Bhats Lemma. Complete, Balanced Factorial Experiments: Models That Admit Restrictions (Finite Models). Models That Do Not Admit Restrictions (Infinite Models). Sum of Squares and Covariance Matrix Algorithms. Expected Mean Squares. Algorithm Applications. Least Squares Regression: Ordinary Least SquaresEstimation. Best Linear Unbiased Estimators. ANOVA Table for the Ordinary Least Squares Regression Function. Weighted Least Squares Regression. Lack of Fit Test. Partitioning the Sum of Squares Regression. The Model Y = X(+ E in Complete, BalancedFactorials. Maximum Likelihood Estimation and Related Topics: Maximum Likelihood Estimators (MLEs) of (and (<+>2. Invariance Property, Sufficiency and Completeness. ANOVA Methods for Finding Maximum Likelihood Estimators. The Likelihood Ratio Test for H(= h. Confidence Bands on Linear Combinations of (. Unbalanced Designs and Missing Data: Replication Matrices. Pattern Matrices and Missing Data. Using Replication and Pattern Matrices Together. Balanced Incomplete Block Designs: General Balanced Incomplete Block Design. Analysis of the General Case. Matrix Derivations of Kempthornes Inter- and Intra-Block Treatment Difference Estimators. Less Than Full Rank Models: Model Assumptions and Examples. The Mean Model Solution. Mean Model Analysis When cov(E) = (<+>2I<->n. Estimable Functions. Mean Model Analysis When cov(E) = (<+>2V. The General Mixed Model: The Mixed Model Structure and Assumptions. Random Portion Analysis: Type I Sumof Squares Method. Random Portion Analysis: Restricted Maximum Likelihood Method. Random Portion Analysis: A Numerical Example. Fixed Portion Analysis. Fixed Portion Analysis: A Numerical Example. Appendixes. References. Subject Index. |
| ctrlnum | (OCoLC)54379581 |
| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocm54379581 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:15:31Z |
| institution | BVB |
| isbn | 058549214X 9780585492148 9780125084659 012508465X 0080510299 9780080510293 |
| language | English |
| oclc_num | 54379581 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 228 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Academic Press, |
| record_format | marc |
| series | Probability and mathematical statistics. |
| series2 | Probability and mathematical statistics |
| spelling | Moser, Barry Kurt. Linear models : a mean model approach / Barry Kurt Moser. San Diego : Academic Press, ©1996. 1 online resource (xii, 228 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Probability and mathematical statistics Includes bibliographical references (pages 221-223) and index. Print version record. Linear Algebra and Related Introductory Topics: Elementary Matrix Concepts. Kronecker Products. Random Vectors. Multivariate Normal Distribution: Multivariate Normal Distribution Function. Conditional Distributionsof Multivariate Normal Vectors. Distributions of Certain Quadratic Forms. Distributions of Quadratic Forms: Quadratic Forms of Normal Random Vectors. Independence. t and F Distributions. Bhats Lemma. Complete, Balanced Factorial Experiments: Models That Admit Restrictions (Finite Models). Models That Do Not Admit Restrictions (Infinite Models). Sum of Squares and Covariance Matrix Algorithms. Expected Mean Squares. Algorithm Applications. Least Squares Regression: Ordinary Least SquaresEstimation. Best Linear Unbiased Estimators. ANOVA Table for the Ordinary Least Squares Regression Function. Weighted Least Squares Regression. Lack of Fit Test. Partitioning the Sum of Squares Regression. The Model Y = X(+ E in Complete, BalancedFactorials. Maximum Likelihood Estimation and Related Topics: Maximum Likelihood Estimators (MLEs) of (and (<+>2. Invariance Property, Sufficiency and Completeness. ANOVA Methods for Finding Maximum Likelihood Estimators. The Likelihood Ratio Test for H(= h. Confidence Bands on Linear Combinations of (. Unbalanced Designs and Missing Data: Replication Matrices. Pattern Matrices and Missing Data. Using Replication and Pattern Matrices Together. Balanced Incomplete Block Designs: General Balanced Incomplete Block Design. Analysis of the General Case. Matrix Derivations of Kempthornes Inter- and Intra-Block Treatment Difference Estimators. Less Than Full Rank Models: Model Assumptions and Examples. The Mean Model Solution. Mean Model Analysis When cov(E) = (<+>2I<->n. Estimable Functions. Mean Model Analysis When cov(E) = (<+>2V. The General Mixed Model: The Mixed Model Structure and Assumptions. Random Portion Analysis: Type I Sumof Squares Method. Random Portion Analysis: Restricted Maximum Likelihood Method. Random Portion Analysis: A Numerical Example. Fixed Portion Analysis. Fixed Portion Analysis: A Numerical Example. Appendixes. References. Subject Index. 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 models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory. Key Features * Provides a versatile format for investigating linear model theory, using the mean model * Uses examples that are familiar to the student: * design of experiments, analysis of variance, regression, and normal distribution theory * Includes a review of relevant linear algebra concepts * Contains fully worked examples which follow the theorem/proof presentation. Linear models (Statistics) http://id.loc.gov/authorities/subjects/sh85077177 MATHEMATICS Probability & Statistics Multivariate Analysis. bisacsh Linear models (Statistics) fast Lineaire modellen. gtt Modèles linéaires (statistique) ram Moyenne. ram Formes quadratiques. ram Analyse de régression Moindres carrés. ram Statistique mathématique. ram Estimation, Théorie de l'. ram Programmation (mathématiques) ram Statistical analysis Print version: Moser, Barry Kurt. Linear models. San Diego : Academic Press, ©1996 012508465X (DLC) 96033930 (OCoLC)34321626 Probability and mathematical statistics. http://id.loc.gov/authorities/names/n42019721 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=91180 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/book/9780125084659 Volltext |
| spellingShingle | Moser, Barry Kurt Linear models : a mean model approach / Probability and mathematical statistics. Linear Algebra and Related Introductory Topics: Elementary Matrix Concepts. Kronecker Products. Random Vectors. Multivariate Normal Distribution: Multivariate Normal Distribution Function. Conditional Distributionsof Multivariate Normal Vectors. Distributions of Certain Quadratic Forms. Distributions of Quadratic Forms: Quadratic Forms of Normal Random Vectors. Independence. t and F Distributions. Bhats Lemma. Complete, Balanced Factorial Experiments: Models That Admit Restrictions (Finite Models). Models That Do Not Admit Restrictions (Infinite Models). Sum of Squares and Covariance Matrix Algorithms. Expected Mean Squares. Algorithm Applications. Least Squares Regression: Ordinary Least SquaresEstimation. Best Linear Unbiased Estimators. ANOVA Table for the Ordinary Least Squares Regression Function. Weighted Least Squares Regression. Lack of Fit Test. Partitioning the Sum of Squares Regression. The Model Y = X(+ E in Complete, BalancedFactorials. Maximum Likelihood Estimation and Related Topics: Maximum Likelihood Estimators (MLEs) of (and (<+>2. Invariance Property, Sufficiency and Completeness. ANOVA Methods for Finding Maximum Likelihood Estimators. The Likelihood Ratio Test for H(= h. Confidence Bands on Linear Combinations of (. Unbalanced Designs and Missing Data: Replication Matrices. Pattern Matrices and Missing Data. Using Replication and Pattern Matrices Together. Balanced Incomplete Block Designs: General Balanced Incomplete Block Design. Analysis of the General Case. Matrix Derivations of Kempthornes Inter- and Intra-Block Treatment Difference Estimators. Less Than Full Rank Models: Model Assumptions and Examples. The Mean Model Solution. Mean Model Analysis When cov(E) = (<+>2I<->n. Estimable Functions. Mean Model Analysis When cov(E) = (<+>2V. The General Mixed Model: The Mixed Model Structure and Assumptions. Random Portion Analysis: Type I Sumof Squares Method. Random Portion Analysis: Restricted Maximum Likelihood Method. Random Portion Analysis: A Numerical Example. Fixed Portion Analysis. Fixed Portion Analysis: A Numerical Example. Appendixes. References. Subject Index. Linear models (Statistics) http://id.loc.gov/authorities/subjects/sh85077177 MATHEMATICS Probability & Statistics Multivariate Analysis. bisacsh Linear models (Statistics) fast Lineaire modellen. gtt Modèles linéaires (statistique) ram Moyenne. ram Formes quadratiques. ram Analyse de régression Moindres carrés. ram Statistique mathématique. ram Estimation, Théorie de l'. ram Programmation (mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85077177 |
| title | Linear models : a mean model approach / |
| title_auth | Linear models : a mean model approach / |
| title_exact_search | Linear models : a mean model approach / |
| title_full | Linear models : a mean model approach / Barry Kurt Moser. |
| title_fullStr | Linear models : a mean model approach / Barry Kurt Moser. |
| title_full_unstemmed | Linear models : a mean model approach / Barry Kurt Moser. |
| title_short | Linear models : |
| title_sort | linear models a mean model approach |
| title_sub | a mean model approach / |
| topic | Linear models (Statistics) http://id.loc.gov/authorities/subjects/sh85077177 MATHEMATICS Probability & Statistics Multivariate Analysis. bisacsh Linear models (Statistics) fast Lineaire modellen. gtt Modèles linéaires (statistique) ram Moyenne. ram Formes quadratiques. ram Analyse de régression Moindres carrés. ram Statistique mathématique. ram Estimation, Théorie de l'. ram Programmation (mathématiques) ram |
| topic_facet | Linear models (Statistics) MATHEMATICS Probability & Statistics Multivariate Analysis. Lineaire modellen. Modèles linéaires (statistique) Moyenne. Formes quadratiques. Analyse de régression Moindres carrés. Statistique mathématique. Estimation, Théorie de l'. Programmation (mathématiques) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=91180 https://www.sciencedirect.com/science/book/9780125084659 |
| work_keys_str_mv | AT moserbarrykurt linearmodelsameanmodelapproach |