Variance Components

Variance Components PDF

Author: Shayle R. Searle

Publisher: John Wiley & Sons

Published: 2009-09-25

Total Pages: 537

ISBN-13: 0470317698

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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . .Variance Components is an excellent book. It is organized and well written, and provides many references to a variety of topics. I recommend it to anyone with interest in linear models." —Journal of the American Statistical Association "This book provides a broad coverage of methods for estimating variance components which appeal to students and research workers . . . The authors make an outstanding contribution to teaching and research in the field of variance component estimation." —Mathematical Reviews "The authors have done an excellent job in collecting materials on a broad range of topics. Readers will indeed gain from using this book . . . I must say that the authors have done a commendable job in their scholarly presentation." —Technometrics This book focuses on summarizing the variability of statistical data known as the analysis of variance table. Penned in a readable style, it provides an up-to-date treatment of research in the area. The book begins with the history of analysis of variance and continues with discussions of balanced data, analysis of variance for unbalanced data, predictions of random variables, hierarchical models and Bayesian estimation, binary and discrete data, and the dispersion mean model.

Estimation of Variance Components and Applications

Estimation of Variance Components and Applications PDF

Author: Calyampudi Radhakrishna Rao

Publisher: North Holland

Published: 1988

Total Pages: 392

ISBN-13:

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Matrix algebra; Asymptotic distribution of quadratic statistics; Variance and covariance components models; Identifiability and estimability; minimum norm quadratic estimation; Pulling of information for estimation; Uniform optimality of minqe's; Computation of minqe's for variance-convariance components models; Integrated minqe and mile; Asymptotic properties estimators; Minimum variance quadratic estimation; Aplications to selection problems.

Linear Models

Linear Models PDF

Author: C.Radhakrishna Rao

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 360

ISBN-13: 1489900241

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The book is based on both authors' several years of experience in teaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results about the definiteness of matrices, especially for the differences of matrices, which enable superiority comparisons of two biased estimates to be made for the first time. We have attempted to provide a unified theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss func tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and its practical applica tions will be useful not only to students but also to researchers and con sultants in statistics.

Analysis of Variance for Random Models, Volume 2: Unbalanced Data

Analysis of Variance for Random Models, Volume 2: Unbalanced Data PDF

Author: Hardeo Sahai

Publisher: Springer Science & Business Media

Published: 2007-07-03

Total Pages: 480

ISBN-13: 0817644253

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Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs with a detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level. It also includes numerical examples to analyze data from a wide variety of disciplines as well as any worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example.

Variance Components

Variance Components PDF

Author: Poduri S.R.S. Rao

Publisher: CRC Press

Published: 1997-06-01

Total Pages: 232

ISBN-13: 9780412728600

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Variance Components Estimation deals with the evaluation of the variation between observable data or classes of data. This is an up-to-date, comprehensive work that is both theoretical and applied. Topics include ML and REML methods of estimation; Steepest-Acent, Newton-Raphson, scoring, and EM algorithms; MINQUE and MIVQUE, confidence intervals for variance components and their ratios; Bayesian approaches and hierarchical models; mixed models for longitudinal data; repeated measures and multivariate observations; as well as non-linear and generalized linear models with random effects.

Parameter Estimation and Hypothesis Testing in Linear Models

Parameter Estimation and Hypothesis Testing in Linear Models PDF

Author: Karl-Rudolf Koch

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 344

ISBN-13: 3662039761

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A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.