Journal ArticleDOI
Mean Square Efficiency of Estimators of Variance Components
TLDR
In this paper, various estimators of components of variance for the balanced one way layout are compared using mean squared error as a measure of performance and several modifications of the maximum likelihood estimator and several formal Bayes estimators are compared and mean square error relationships are given.Abstract:
Various estimators of components of variance for the balanced one way layout are compared using mean squared error as a measure of performance. Several modifications of the maximum likelihood estimator and several formal Bayes estimators are compared and mean square error relationships are given. Inadmissibility is established for a large class of translation and scale invariant estimators. Numerical results are tabled and graphed to exhibit the relative efficiency of the estimators considered.read more
Citations
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Journal ArticleDOI
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
TL;DR: In this paper, the authors proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects, and developed a satisfactory asymptotic theory for estimators of variance components.
Journal ArticleDOI
A comparison of Bayesian and likelihood-based methods for fitting multilevel models
William J Browne,David Draper +1 more
TL;DR: The Bayesian and likelihood-based methods studied are considerably faster computationally than MCMC, and steady improvements in recent years in both hardware speed and e-ciency of MonteCarloalgorithms are steady.
Journal ArticleDOI
Bayesian Methods in Animal Breeding Theory
Daniel Gianola,Rohan L. Fernando +1 more
TL;DR: In this paper, a general framework for estimating breeding value with or without selection or assortative mating, including the situation where variances and covarianees are unknown, is presented.
Journal ArticleDOI
A Comparison of Variance Component Estimators
R. R. Corbeil,Shayle R. Searle +1 more
TL;DR: These studies and those of Klotz, Milton and Zacks point, with some exceptions, to the greater efficiency of ML estimators under a range of experimental settings.
Journal ArticleDOI
Variance Components Analysis: A Selective Literature Survey
André I. Khuri,Hardeo Sahai +1 more
TL;DR: In this article, a survey is given of developments in the area of variance components during the last three decades, covering mainly point estimation, interval estimation, and hypothesis testing concerning the variance components for both balanced and unbalanced models.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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The Analysis of Variance
TL;DR: In this paper, the basic theory of analysis of variance by considering several different mathematical models is examined, including fixed-effects models with independent observations of equal variance and other models with different observations of variance.
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A Note on the Generation of Random Normal Deviates
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Tables of Integrals
TL;DR: In the fourth edition of the book as mentioned in this paper, the section on definite integrals has been considerably enlarged and a section added on integrals essentially of elliptic type, which is the case with the present edition.