Statistical tests in mixed linear models [[electronic resource] /] / André I. Khuri, Thomas Mathew, Bimal K. Sinha

• Autore: Khuri André I. <1940->
• Pubblicazione: New York, : Wiley, c1998
• Descrizione fisica: 1 online resource (378 p.)
• Disciplina: 519.5
• Soggetto topico: Linear models (Statistics); Statistical hypothesis testing
• Soggetto genere / forma: Electronic books.
• Altri autori: MathewThomas <1955-> SinhaBimal K. <1946->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 335-343) and indexes.
• Nota di contenuto: Statistical Tests for Mixed Linear Models; Contents; Preface; 1. Nature of Exact and Optimum Tests in Mixed Linear Models; 1.1. Introduction; 1.2. Exact F-Tests; 1.3. Optimality of Tests; 1.3.1. Uniformly Most Powerful Similar and Uniformly Most Powerful Unbiased Tests; 1.3.2. Uniformly Most Powerful Invariant and Locally Most Powerful or Locally Best Invariant Tests; Appendix 1.1. Distribution of a Maximal Invariant T (x): Wijsman's Representation Theorem; Bibliography; 2. Balanced Random and Mixed Models; 2.1. Introduction; 2.2. Balanced Models - Notations and Definitions ; 2.3. Balanced Model Properties2.4. Balanced Mixed Models: Distribution Theory; 2.5. Derivation of Optimum Tests; 2.5.1. A Numerical Example; 2.6. Approximate and Exact Tests; 2.6.1. Satterthwaite's Approximation; 2.6.2. Exact Unbiased Tests of Bartlett-Scheffé Type; Exercises; Bibliography; 3. Measures of Data Imbalance; 3.1. Introduction; 3.2. The Effects of Imbalance; 3.2.1. The Variance of σ2τ; 3.2.2. The Probability of a Negative σ2τ; 3.2.3. Power of the Test Concerning σ2τ; 3.3. Measures of Imbalance for the One-Way Model; 3.3.1. The Effect of Imbalance on Var(σ2τ) ; 3.3.2. The Effect of Imbalance on the Test Concerning σ2τ3.4. A General Procedure For Measuring Imbalance; 3.4.1. The One-Way Classification Model; 3.4.2. The Two-Way Classification Model; 3.4.3. The Three-Way Classification Model; 3.5. Special Types of Imbalance; 3.5.1. The Two-Fold Nested Classification Model; 3.5.2. A Model With a Mixture of Cross-Classified and Nested Effects; 3.6. A General Method for Determining the Effect of Imbalance; 3.6.1. Generation of Designs Having a Specified Degree of Imbalance for the One-Way Model; 3.6.2. An Example; 3.7. Summary ; Appendix 3.1. Hirotsu's ApproximationExercises; Bibliography; 4. Unbalanced One-Way and Two-Way Random Models; 4.1. Introduction; 4.2. Unbalanced One-Way Random Models; 4.3. Two-Way Random Models; 4.3.1. Models Without Interaction: Exact Tests; 4.3.2. Models Without Interaction: Optimum Tests; 4.3.3. Models With Interaction: Exact Tests; 4.3.4. A Numerical Example; 4.4. Random Two-Fold Nested Models; 4.4.1. Testing Hβ(τ) : σ2β(τ) = 0; 4.4.2. Testing Hτ : σ2τ = 0; Exercises; Bibliography; 5. Random Models with Unequal Cell Frequencies in the Last Stage; 5.1. Introduction ; 5.2. Unbalanced Random Models With Imbalance In The Last Stage Only-Notation5.3. Unbalanced Random Models With Imbalance In The Last Stage Only-Analysis; 5.3.1. Derivation of Exact Tests; 5.4. More on Exact Tests; 5.4.1. Power of the Exact Tests; 5.4.2. Sufficient Statistics Associated With the Exact Tests; 5.5. A Numerical Example; Exercises; Bibliography; 6. Tests in Unbalanced Mixed Models; 6.1. Introduction; 6.2. Mixed Models With Two Variance Components; 6.2.1. Test for Hτ : τ1 = ... = τυ; 6.2.2. Optimum Test for Hτ : σ2τ = 0 ; 6.3. Mixed Two-Way Crossed-Classification Models With Interactions
• Sommario/riassunto: An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these
• Titolo autorizzato: Statistical tests in mixed linear models
• ISBN: 1-283-27397-7; 9786613273970; 1-118-16486-5; 1-118-16485-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910139594203321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley series in probability and statistics. . -Applied probability and statistics.