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Titre : Estimation of variance components and applications Type de document : Monographie Auteurs : Calyampudi Radhakrishna Rao, Auteur ; J. Kleffe, Auteur Editeur : Amsterdam [Pays Bas] : Elsevier Année de publication : 1988 Collection : North-Holland series in statisticsand probability num. 3 Importance : 370 p. Format : 16 x 23 cm ISBN/ISSN/EAN : 978-0-444-70023-0 Note générale : Bibliographie Langues : Français (fre) Descripteur : [Vedettes matières IGN] Statistiques
[Termes IGN] asymptote
[Termes IGN] calcul matriciel
[Termes IGN] covariance
[Termes IGN] méthode des moindres carrés
[Termes IGN] probabilités
[Termes IGN] varianceNote de contenu : PREFACE
1. Historical review
2. Outline of the present monograph
References
CHAPTER 1 MATRIX ALGEBRA
1.1. Notation and basic results
1.2. Generalized inverse of matrices
1.3. Orthogonal projection
1.4. Matrix products
1.5. Representation of matrices by vectors
1.6. Quadratic subspaces
1.7. Quasi inner products
1.8. Complements and problems
CHAPTER 2 ASYMPTOTIC DISTRIBUTION OF QUADRATIC STATISTICS
2.1. Fourth order moments of quadratic statistics
2.2. Cumulants of quadratic forms of normal variables
2.3. Inequalities on moments of quadratic forms
2 4. Consistency of linear and quadratic functions of independent random variables
2.5. Asymptotic normality
2.6. Complements and problems
CHAPTER 3 VARIANCE AND COVAPIANCE COMPONENTS MODELS
3.1. Extensions of the GaussMarkoff model
3.2. A general model
3.3. Models for two way classification data
3.4. Variance and covariance components
3.5. Autoregressive random effects
3.6. A general random effects model
3.7. A general multivariate model
3.8. Complements and problems
CHAPTER 4 IDENTIFIABILITY AND ESTIMABILITY
4.1. Notation
4.2. Identifiability
4.3. Unbiased estimability
4.4. Invariant estimability
4.5. Estimability of covariance parameters in growth curve models
4.6. Complements and problems
CHAPTER 5 MINIMUM NORM QUADRATIC ESTIMATION
5.1. The principle of MINQE
5.2. MINQE (U, 1)
5.3. MINQE (U)
5.4. - MINQE (U)
5.5. MINQE without unbiasedness
5.6. MINQE (U, NND)
5.7. Complements and problems
CHAPTER 6 POOLING OF INFORMATION FOR ESTIMATION
6.1. Replicated model
6.2. Models with block structure
6.3. Models with a common mean
6.4. Complements and problems
CHAPTER 7 UNIFORM OPTIMALITY OF MINQE'S
7. 1. Uniform optimality of MINQE (U, 1)
7.2. Uniform optimality of MINOE (U)
7.3. Pooled observations
7.4. Balanced ANOVA models
7.5. Complements and problems
CHAPTER 8 COMPUTATION OF MINQE'S FOR VARIANCECOVARIANCE COMPONENTS MODELS
8.1. The principal scheme of computations
8.2. Generalized hierarchical models
8.3. Some extensions of the algorithm
8.4. Nested classification model
8.5. Complements and problems
CHAPTER 9 ITERATED MINQE AND MLE
9.1. Iterated MINQE (IMINQE)
9.2. Maximum likelihood estimation (MLE)
9.3. Marginal MLE (MMLE)
9.4. Computation of NILE
9.5. Computation of the loglikelihood function
9.6. Complements and problems
CHAPTER 10 ASYMPTOTIC PROPERTIES OF ESTIMATORS
10.1. Introduction
10.2. Consistency of MINOE
10.3. Asymptotic normality of MINQE (U,I) and MINQE (I)
10.4. Replicated error structure
10.5. Some results on iterated NIME
10.6. Efficiency of iterated MINQE under normality
10.7. Large sample tests and confidence regions
10.8. Complements and problems
CHAPTER 11 MINIMUM VARIANCE OUADRATIC ESTIMATION
11.1. Locally best quadratic estimators
11.2. Bayes quadratic estimates under normal distribution
11.3. Hsu's theorem and extensions
11.4. Complements and problems
CHAPTER 12 APPLICATIONS TO SELECTION PROBLEMS
12.1. Selection rules
12.2. Simultaneous prediction in linear models
12.3. Simultaneous prediction in a multivariate case
12.4. Estimation in a mixed linear model
12.5. Complements and problemsNuméro de notice : 65751 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Monographie DOI : sans Accessibilité hors numérique : Accessible via le SUDOC (sur demande au cdos) Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=61474 Exemplaires(1)
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