Sahai, Hardeo; Ojeda, Mario Miguel Analysis of variance for random models. Vol. 1: Balanced data. Theory, methods, applications, and data analysis. (English) Zbl 1076.62075 Boston: Birkhäuser (ISBN 0-8176-3230-1/hbk). xxv, 484 p. (2004). Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences.This book considers the balanced data. It is devoted mainly to the study of random effects models. It provides comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. In Chapter 1, it briefly introduces analysis of variance models, fixed effects models, random effects models, mixed effects models, variance components and their applications. In Chapter 2, one-way classification is studied. In Chapter 3, two-way crossed classification without interaction is considered. Chapter 4 is devoted to the study of two-way classifications with interactions. Three-way and higher-order crossed classifications are investigated in Chapter 5. In Chapter 6, two-way nested classification is discussed, while three-way and higher-order nested classifications are covered in Chapter 7. The discussion of general balanced random effects model is provided in Chapter 8. Some useful materials are given in the Appendices. In this book, one can find some numerical examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP. Exercises and references related to the chapter contents are provided at the end of each chapter. This book is accessible to readers with only a modest mathematical and statistical background. The work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis. Reviewer: Yuehua Wu (Toronto) Cited in 1 ReviewCited in 7 Documents MSC: 62J10 Analysis of variance and covariance (ANOVA) 62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics 62Pxx Applications of statistics Keywords:Analysis of variance model; fixed effects model; random effects model; mixed effects model; variance component; one-way classification; two-way classification; three-way classification; higher-order crossed classification; nested classification; interaction; minimum sufficient statistic; maximum likelihood estimator; Stein-type estimator; Federer’s nontruncated exponential corrector estimator; Naqvi’s goodness-of-fit estimator; Hodges-Lehmann-type estimator; minimum variance unbiased estimator; Bayesian estimation; mean squared error criterion; interval estimation; confidence interval; optimum sample size; Anderson-Bancroft procedure; Bartlett-Scheffé test; Bayes equivalent estimator; Bayes risk; Chi-square; empirical Bayes quadratic estimator; Edgeworth series expansion; EM algorithm; Fisher scoring iteration; finite population model; block design; Graeco-Latin square; Graybill-Wang procedure; Healy procedure; Howe procedure; TBGJL procedure; Hessian; hierarchical design; Kuhn-Tucker condition; Kurtosis; Latin square; lognormal distribution; Milliken-Johnson formula; Moriguti-Bulmer procedure; Myers-Howe procedure; Newton-Raphson iteration; Satterthwaite procedure; split-plot design; uniformly most powerful unbiased; Welch-Boardman procedure; Welch method; Williams procedure Software:SAS; SPSS; BMDP PDFBibTeX XMLCite \textit{H. Sahai} and \textit{M. M. Ojeda}, Analysis of variance for random models. Vol. 1: Balanced data. Theory, methods, applications, and data analysis. Boston: Birkhäuser (2004; Zbl 1076.62075)