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Estimation of variance components and applications / Calyampudi Radhakrishna Rao (1988)

Public 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] variance Note 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 problems Numéro 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

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Linear statistical inference and its applications / Calyampudi Radhakrishna Rao (1973)

Public Titre : Linear statistical inference and its applications Type de document : Monographie Auteurs : Calyampudi Radhakrishna Rao, Auteur Editeur : New York, Londres, Hoboken (New Jersey), ... : John Wiley & Sons Année de publication : 1973 Importance : 625 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-0-471-70823-0 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques [Termes IGN] analyse discriminante [Termes IGN] calcul matriciel [Termes IGN] covariance [Termes IGN] espace vectoriel [Termes IGN] estimation statistique [Termes IGN] inférence statistique [Termes IGN] matrice [Termes IGN] méthode des moindres carrés [Termes IGN] modèle stochastique [Termes IGN] probabilités [Termes IGN] statistique mathématique [Termes IGN] variable aléatoire [Termes IGN] variance Numéro de notice : 56080 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=59967