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Variance Components

Variance Components
Author: Shayle R. Searle
Publisher: John Wiley & Sons
Total Pages: 537
Release: 2009-09-25
Genre: Mathematics
ISBN: 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.


Variance Components

Variance Components
Author: Poduri S.R.S. Rao
Publisher: CRC Press
Total Pages: 232
Release: 1997-06-01
Genre: Mathematics
ISBN: 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.


Estimation of Variance Components and Applications

Estimation of Variance Components and Applications
Author: Calyampudi Radhakrishna Rao
Publisher: North Holland
Total Pages: 392
Release: 1988
Genre: Business & Economics
ISBN:

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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.


Design and Analysis of Long-term Ecological Monitoring Studies

Design and Analysis of Long-term Ecological Monitoring Studies
Author: Robert A. Gitzen
Publisher: Cambridge University Press
Total Pages: 779
Release: 2012-06-07
Genre: Nature
ISBN: 1139510193

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To provide useful and meaningful information, long-term ecological programs need to implement solid and efficient statistical approaches for collecting and analyzing data. This volume provides rigorous guidance on quantitative issues in monitoring, with contributions from world experts in the field. These experts have extensive experience in teaching fundamental and advanced ideas and methods to natural resource managers, scientists and students. The chapters present a range of tools and approaches, including detailed coverage of variance component estimation and quantitative selection among alternative designs; spatially balanced sampling; sampling strategies integrating design- and model-based approaches; and advanced analytical approaches such as hierarchical and structural equation modelling. Making these tools more accessible to ecologists and other monitoring practitioners across numerous disciplines, this is a valuable resource for any professional whose work deals with ecological monitoring. Supplementary example software code is available online at www.cambridge.org/9780521191548.


Variance Component Estimation with Model-based Diagnostics

Variance Component Estimation with Model-based Diagnostics
Author: Ronald R. Hocking
Publisher:
Total Pages: 70
Release: 1988
Genre: Analysis of variance
ISBN:

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The problem of estimating variance components in mixed linear models has no satisfactory solution for the unbalanced data case. Further, there has been little work on diagnostic methods for assessing the data and the model. In this article, we propose a new class of unbiased estimators. These estimators have simple closed form expressions allowing for small sample analysis and easy computations. The structure of the estimators reveals natural diagnostics for examining the data and the model assumptions. The source of negative estimates of variance components is revealed. Limited efficiency studies indicate that these estimators are comparable to existing estimators. The estimators are illustrated by two numerical examples that reveal the importance of the diagnostic analysis.


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

Analysis of Variance for Random Models, Volume 2: Unbalanced Data
Author: Hardeo Sahai
Publisher: Springer Science & Business Media
Total Pages: 493
Release: 2007-07-03
Genre: Mathematics
ISBN: 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.